SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                  SCHEDULE 13G
                                 (Rule 13d-102)

 INFORMATION TO BE INCLUDED IN STATEMENTS FILED PURSUANT TO RULES 13d-1(b), (c),
         AND (d) AND AMENDMENTS THERETO FILED PURSUANT TO RULE 13d-2(b)
                               (Amendment No. 2)*







                               UNISYS Corporation
--------------------------------------------------------------------------------
                                (Name of Issuer)



                          Common Stock, $0.01 par value
--------------------------------------------------------------------------------
                         (Title of Class of Securities)



                                    909214108
--------------------------------------------------------------------------------
                                 (CUSIP Number)



                                 March 23, 2006
--------------------------------------------------------------------------------
             (Date of Event which Requires Filing of this Statement)


Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

         [ ]      Rule 13d-1(b)

         [X]      Rule 13d-1(c)

         [ ]      Rule 13d-1(d)



* The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).


                                     Page 1

<PAGE>


CUSIP No.  909214108
           ----------------------

--------------------------------------------------------------------------------

    1)   Names of Reporting Person

         S.S. or I.R.S. Identification No. of Above Person

              Tudor Investment Corporation
         -----------------------------------------------------------------------
              22-2514825
         -----------------------------------------------------------------------

--------------------------------------------------------------------------------

    2)   Check the Appropriate Box if a Member of a Group (See Instructions)
         (a)
              ------------------------------------------------------------------

         (b)         X
              ------------------------------------------------------------------

--------------------------------------------------------------------------------

    3)   SEC Use Only
                      ----------------------------------------------------------

--------------------------------------------------------------------------------

    4)   Citizenship or Place of Organization      Delaware
                                               ---------------------------------

--------------------------------------------------------------------------------

                      (5)  Sole Voting Power                            0
                                              ----------------------------------
Number of Shares      ----------------------------------------------------------
Beneficially          (6)  Shared Voting Power                 14,538,686
Owned by Each                                   --------------------------------
Reporting Person      ----------------------------------------------------------
With                  (7)  Sole Dispositive Power                       0
                                                   -----------------------------
                      ----------------------------------------------------------
                      (8)  Shared Dispositive Power            14,538,686
                                                    ----------------------------

--------------------------------------------------------------------------------

    9)   Aggregate Amount Beneficially Owned by Each Reporting
         Person                                                14,538,686
               -----------------------------------------------------------------

--------------------------------------------------------------------------------

   10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares
         (See Instructions)
                            ----------------------------------------------------

--------------------------------------------------------------------------------

   11)   Percent of Class Represented by Amount in Row 9             4.3%
                                                               -----------------

--------------------------------------------------------------------------------

   12)   Type of Reporting Person (See Instructions)        CO
                                                      --------------------------

--------------------------------------------------------------------------------


                                     Page 2


<PAGE>


CUSIP No.  909214108
           ----------------------

--------------------------------------------------------------------------------

    1)   Names of Reporting Person

         S.S. or I.R.S. Identification No. of Above Person

              Paul Tudor Jones, II
         -----------------------------------------------------------------------

         -----------------------------------------------------------------------

--------------------------------------------------------------------------------

    2)   Check the Appropriate Box if a Member of a Group (See Instructions)
         (a)
              ------------------------------------------------------------------

         (b)         X
              ------------------------------------------------------------------

--------------------------------------------------------------------------------

    3)   SEC Use Only
                      ----------------------------------------------------------

--------------------------------------------------------------------------------

    4)   Citizenship or Place of Organization      USA
                                               ---------------------------------

--------------------------------------------------------------------------------

                      (5)  Sole Voting Power                            0
                                              ----------------------------------
Number of Shares      ----------------------------------------------------------
Beneficially          (6)  Shared Voting Power                 15,851,300
Owned by Each                                   --------------------------------
Reporting Person      ----------------------------------------------------------
With                  (7)  Sole Dispositive Power                       0
                                                   -----------------------------
                      ----------------------------------------------------------
                      (8)  Shared Dispositive Power            15,851,300
                                                    ----------------------------

--------------------------------------------------------------------------------

    9)   Aggregate Amount Beneficially Owned by Each Reporting
         Person                                                15,851,300
               -----------------------------------------------------------------

--------------------------------------------------------------------------------

   10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares
         (See Instructions)
                            ----------------------------------------------------

--------------------------------------------------------------------------------

   11)   Percent of Class Represented by Amount in Row 9             4.6%
                                                               -----------------

--------------------------------------------------------------------------------

   12)   Type of Reporting Person (See Instructions)        IN
                                                      --------------------------

--------------------------------------------------------------------------------


                                     Page 3


<PAGE>


CUSIP No.  909214108
           ----------------------

--------------------------------------------------------------------------------

    1)   Names of Reporting Person

         S.S. or I.R.S. Identification No. of Above Person

              Tudor Proprietary Trading, L.L.C.
         -----------------------------------------------------------------------
              13-3720063
         -----------------------------------------------------------------------

--------------------------------------------------------------------------------

    2)   Check the Appropriate Box if a Member of a Group (See Instructions)
         (a)
              ------------------------------------------------------------------

         (b)         X
              ------------------------------------------------------------------

--------------------------------------------------------------------------------

    3)   SEC Use Only
                      ----------------------------------------------------------

--------------------------------------------------------------------------------

    4)   Citizenship or Place of Organization      Delaware
                                               ---------------------------------

--------------------------------------------------------------------------------

                      (5)  Sole Voting Power                            0
                                              ----------------------------------
Number of Shares      ----------------------------------------------------------
Beneficially          (6)  Shared Voting Power                  1,312,614
Owned by Each                                   --------------------------------
Reporting Person      ----------------------------------------------------------
With                  (7)  Sole Dispositive Power                       0
                                                   -----------------------------
                      ----------------------------------------------------------
                      (8)  Shared Dispositive Power             1,312,614
                                                    ----------------------------

--------------------------------------------------------------------------------

    9)   Aggregate Amount Beneficially Owned by Each Reporting
         Person                                                 1,312,614
               -----------------------------------------------------------------

--------------------------------------------------------------------------------

   10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares
         (See Instructions)
                            ----------------------------------------------------

--------------------------------------------------------------------------------

   11)   Percent of Class Represented by Amount in Row 9             0.4%
                                                               -----------------

--------------------------------------------------------------------------------

   12)   Type of Reporting Person (See Instructions)        OO
                                                      --------------------------

--------------------------------------------------------------------------------


                                     Page 4


<PAGE>


CUSIP No.  909214108
           ----------------------

--------------------------------------------------------------------------------

    1)   Names of Reporting Person

         S.S. or I.R.S. Identification No. of Above Person

         The Tudor BVI Global Portfolio Ltd.
         -----------------------------------------------------------------------

         -----------------------------------------------------------------------

--------------------------------------------------------------------------------

    2)   Check the Appropriate Box if a Member of a Group (See Instructions)
         (a)
              ------------------------------------------------------------------

         (b)         X
              ------------------------------------------------------------------

--------------------------------------------------------------------------------

    3)   SEC Use Only
                      ----------------------------------------------------------

--------------------------------------------------------------------------------

    4)   Citizenship or Place of Organization      Cayman Islands
                                               ---------------------------------

--------------------------------------------------------------------------------

                      (5)  Sole Voting Power                            0
                                              ----------------------------------
Number of Shares      ----------------------------------------------------------
Beneficially          (6)  Shared Voting Power                  2,444,334
Owned by Each                                   --------------------------------
Reporting Person      ----------------------------------------------------------
With                  (7)  Sole Dispositive Power                       0
                                                   -----------------------------
                      ----------------------------------------------------------
                      (8)  Shared Dispositive Power             2,444,334
                                                    ----------------------------

--------------------------------------------------------------------------------

    9)   Aggregate Amount Beneficially Owned by Each Reporting
         Person                                                 2,444,334
               -----------------------------------------------------------------

--------------------------------------------------------------------------------

   10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares
         (See Instructions)
                            ----------------------------------------------------

--------------------------------------------------------------------------------

   11)   Percent of Class Represented by Amount in Row 9             0.7%
                                                               -----------------

--------------------------------------------------------------------------------

   12)   Type of Reporting Person (See Instructions)        CO
                                                      --------------------------

--------------------------------------------------------------------------------


                                     Page 5


<PAGE>


CUSIP No.  909214108
           ----------------------

--------------------------------------------------------------------------------

    1)   Names of Reporting Person

         S.S. or I.R.S. Identification No. of Above Person

         The Raptor Global Portfolio Ltd.
         -----------------------------------------------------------------------

         -----------------------------------------------------------------------

--------------------------------------------------------------------------------

    2)   Check the Appropriate Box if a Member of a Group (See Instructions)
         (a)
              ------------------------------------------------------------------

         (b)         X
              ------------------------------------------------------------------

--------------------------------------------------------------------------------

    3)   SEC Use Only
                      ----------------------------------------------------------

--------------------------------------------------------------------------------

    4)   Citizenship or Place of Organization      Cayman Islands
                                               ---------------------------------

--------------------------------------------------------------------------------

                      (5)  Sole Voting Power                            0
                                              ----------------------------------
Number of Shares      ----------------------------------------------------------
Beneficially          (6)  Shared Voting Power                 11,986,309
Owned by Each                                   --------------------------------
Reporting Person      ----------------------------------------------------------
With                  (7)  Sole Dispositive Power                       0
                                                   -----------------------------
                      ----------------------------------------------------------
                      (8)  Shared Dispositive Power            11,986,309
                                                    ----------------------------

--------------------------------------------------------------------------------

    9)   Aggregate Amount Beneficially Owned by Each Reporting
         Person                                                11,986,309
               -----------------------------------------------------------------

--------------------------------------------------------------------------------

   10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares
         (See Instructions)
                            ----------------------------------------------------

--------------------------------------------------------------------------------

   11)   Percent of Class Represented by Amount in Row 9             3.5%
                                                               -----------------

--------------------------------------------------------------------------------

   12)   Type of Reporting Person (See Instructions)        CO
                                                      --------------------------

--------------------------------------------------------------------------------


                                     Page 6

<PAGE>


CUSIP No.  909214108
           ----------------------

--------------------------------------------------------------------------------

    1)   Names of Reporting Person

         S.S. or I.R.S. Identification No. of Above Person

         The Altar Rock Fund L.P.
         -----------------------------------------------------------------------
         06-1558414
         -----------------------------------------------------------------------

--------------------------------------------------------------------------------

    2)   Check the Appropriate Box if a Member of a Group (See Instructions)
         (a)
              ------------------------------------------------------------------

         (b)         X
              ------------------------------------------------------------------

--------------------------------------------------------------------------------

    3)   SEC Use Only
                      ----------------------------------------------------------

--------------------------------------------------------------------------------

    4)   Citizenship or Place of Organization      Delaware
                                               ---------------------------------

--------------------------------------------------------------------------------

                      (5)  Sole Voting Power                            0
                                              ----------------------------------
Number of Shares      ----------------------------------------------------------
Beneficially          (6)  Shared Voting Power                    108,043
Owned by Each                                   --------------------------------
Reporting Person      ----------------------------------------------------------
With                  (7)  Sole Dispositive Power                       0
                                                   -----------------------------
                      ----------------------------------------------------------
                      (8)  Shared Dispositive Power               108,043
                                                    ----------------------------

--------------------------------------------------------------------------------

    9)   Aggregate Amount Beneficially Owned by Each Reporting
         Person                                                   108,043
               -----------------------------------------------------------------

--------------------------------------------------------------------------------

   10)   Check if the Aggregate Amount in Row (9) Excludes Certain Shares
         (See Instructions)
                            ----------------------------------------------------

--------------------------------------------------------------------------------

   11)   Percent of Class Represented by Amount in Row 9             0.03%
                                                               -----------------

--------------------------------------------------------------------------------

   12)   Type of Reporting Person (See Instructions)        PN
                                                      --------------------------

--------------------------------------------------------------------------------


                                     Page 7

<PAGE>


Item 1(a).  Name of Issuer:

            UNISYS Corporation

Item 1(b).  Address of Issuer's Principal Executive Offices:

            Unisys Way
            Blue Bell, PA  19424

Item 2(a).  Name of Person Filing:

            Tudor Investment Corporation ("TIC")
            Paul Tudor Jones, II
            Tudor Proprietary Trading, L.L.C. ("TPT")
            The Tudor BVI Global Portfolio Ltd. ("BVI Portfolio")
            The Raptor Global Portfolio Ltd. ("Raptor Portfolio")
            The Altar Rock Fund L.P. ("Altar Rock")

Item 2(b).  Address of Principal Business Office or, if none, Residence:

            The principal business office of each of TIC, TPT, and Altar Rock
is:

                        1275 King Street
                        Greenwich, CT 06831

            The principal business office of Mr. Jones is:

                        c/o Tudor Investment Corporation
                        1275 King Street
                        Greenwich, CT 06831

            The principal business office of each of Raptor Portfolio and BVI
Portfolio is:

                        c/o CITCO
                        Kaya Flamboyan 9
                        P.O. Box 4774
                        Curacao, Netherlands Antilles

Item 2(c).  Citizenship:

            TIC is a Delaware corporation.
            Mr. Jones is a citizen of the United States.
            TPT is a Delaware limited liability company.
            Altar Rock is a Delaware limited partnership.
            Raptor Portfolio and BVI Portfolio are companies organized under
the laws of the Cayman Islands.

Item 2(d).  Title of Class of Securities:

            Common Stock, par value $0.01

Item 2(e).  CUSIP Number:

            909214108


                                     Page 8

<PAGE>


Item 3.     If this statement is filed pursuant to Rules 13d-1(b), or 13d-2(b),
            check whether the person filing is a:
            (a)  [ ]  Broker or Dealer registered under section 15 of the Act
            (b)  [ ]  Bank as defined in section 3(a)(6) of the Act
            (c)  [ ]  Insurance Company as defined in section 3(a)(19) of the
                      Act
            (d)  [ ]  Investment Company registered under section 8 of the
                      Investment Company Act
            (e)  [ ]  Investment Adviser registered under section 203 of the
                      Investment Advisers Act of 1940
            (f)  [ ]  Employment Benefit Plan, Pension Fund which is subject to
                      the provisions of the Employee Retirement Income Security
                      Act of 1974 or Endowment Fund; see section
                      240.13d-1(b)(1)(ii)(F)
            (g)  [ ]  Parent Holding Company, in accordance with section
                      240.13d-1(b)(1)(ii)(G) (Note: See Item 7)
            (h)  [ ]  Group, in accordance with section 240.13d-1(b)(1)(ii)(H)

Item 4.     Ownership (As of March 30, 2006).

            (a) Amount Beneficially Owned: See Item 9 of cover pages

            (b) Percent of Class: See Item 11 of cover pages

            (c) Number of shares as to which such person has:

                (i)   sole power to vote or to direct the vote
                      See Item 5 of cover pages
                      ----------------------------------------------------------

                (ii)  shared power to vote or to direct the vote
                      See Item 6 of cover pages
                      ----------------------------------------------------------

                (iii) sole power to dispose or to direct the disposition of
                      See Item 7 of cover pages
                      ----------------------------------------------------------

                (iv)  shared power to dispose or to direct the disposition of
                      See Item 8 of cover pages
                      ----------------------------------------------------------

                The shares of Common Stock reported herein as beneficially owned
            are owned directly by TPT (1,312,614 shares), Raptor Portfolio
            (11,986,309 shares), BVI Portfolio (2,444,334 shares), and Altar
            Rock (108,043 shares). Because TIC provides investment advisory
            services to Raptor Portfolio and BVI Portfolio and is the general
            partner of Altar Rock, TIC may be deemed to beneficially own the
            shares of Common Stock owned by each of such Reporting Persons. TIC
            expressly disclaims such beneficial ownership. In addition, because
            Mr. Jones is the controlling shareholder of TIC and the indirect
            controlling equity holder of TPT, Mr. Jones may be deemed to
            beneficially own the shares of Common Stock deemed beneficially
            owned by TIC and TPT. Mr. Jones expressly disclaims such beneficial
            ownership.

Item 5.     Ownership of Five Percent or Less of a Class.

                   If this statement is being filed to report that as of the
date hereof the reporting person has ceased to be the beneficial owner of more
than five percent of the class of securities, check the following [X].


Item 6.     Ownership of More than Five Percent on Behalf of Another Person.

                   Not applicable

Item 7.     Identification and Classification of the Subsidiary Which Acquired
            the Security Being Reported on By the Parent Holding Company.

                   Not applicable

Item 8.     Identification and Classification of Members of the Group.

                   See cover pages

Item 9.     Notice of Dissolution of Group.

                   Not applicable


                                      Page 9



<PAGE>


Item 10.  Certification.

                   By signing below I certify that, to the best of my knowledge
and belief, the securities referred to above were not acquired and are not held
for the purpose of or with the effect of changing or influencing the control of
the issuer of the securities and were not acquired and are not held in
connection with or as a participant in any transaction having that purpose or
effect.

                   After reasonable inquiry and to the best of my knowledge and
belief, I certify that the information set forth in this statement is true,
complete and correct.


                            Dated:       March 31, 2006


                            TUDOR INVESTMENT CORPORATION


                            By:          /s/ Stephen N. Waldman
                                 -----------------------------------------------
                                 Stephen N. Waldman
                                 Managing Director and Associate General Counsel



                                         /s/ Paul Tudor Jones, II
                            ----------------------------------------------------
                                         Paul Tudor Jones, II



                            TUDOR PROPRIETARY TRADING, L.L.C.


                            By:          /s/ Stephen N. Waldman
                                 -----------------------------------------------
                                 Stephen N. Waldman
                                 Managing Director and Associate General Counsel


                            THE TUDOR BVI GLOBAL PORTFOLIO LTD.

                            By:   Tudor Investment Corporation,
                                  Trading Advisor

                                By:      /s/ Stephen N. Waldman
                                     -------------------------------------------
                                     Stephen N. Waldman
                                     Managing Director and Associate General
                                       Counsel


                                    Page 10


<PAGE>


                            THE RAPTOR GLOBAL PORTFOLIO LTD.

                            By:   Tudor Investment Corporation,
                                  Investment Advisor


                                By:      /s/ Stephen N. Waldman
                                     -------------------------------------------
                                     Stephen N. Waldman
                                     Managing Director and Associate General
                                       Counsel


                            THE ALTAR ROCK FUND L.P.

                            By:   Tudor Investment Corporation,
                                  General Partner


                                By:      /s/ Stephen N. Waldman
                                     -------------------------------------------
                                     Stephen N. Waldman
                                     Managing Director and Associate General
                                       Counsel


                                    Page 11