<PAGE>
 
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                   --------

                                    FORM 8-K

                                 CURRENT REPORT

                    Pursuant to Section 13 OR 15(d) of the
                         Securities Exchange Act of 1934

Date of Report (Date of Earliest Event Reported)            December 7, 2000
----------------------------------------------------------------------------


                               UNISYS CORPORATION
---------------------------------------------------------------------------
           (Exact Name of Registrant as Specified in its Charter)



   Delaware                  1-8729                    38-0387840
---------------------------------------------------------------------------
(State or Other      (Commission File Number)        (IRS Employer
Jurisdiction of                                    Identification No.)
Incorporation)



                                   Unisys Way
                          Blue Bell, Pennsylvania 19424
---------------------------------------------------------------------------
           (Address of Principal Executive Offices)  (Zip Code)



                                 (215) 986-4011
---------------------------------------------------------------------------
          (Registrant's telephone number, including area code)

<PAGE>
 

Item 5.    Other Events.

           On December 7, 2000, the Board of Directors of Unisys Corporation
(the "Company") extended the Company's Preferred Share Purchase Rights (the
"Rights") for five additional years. The Rights are now set to expire on March
17, 2006.


Item 7.    Exhibits.

4          Amendment No. 2, dated as of December 7, 2000, to the Rights
           Agreement, dated as of March 7, 1986, between Unisys Corporation
           (then named Burroughs Corporation) and Harris Trust Company of New
           York, as Rights Agent, as amended on February 22, 1996, and as
           further amended on January 10, 2000.

<PAGE>
 

                                    SIGNATURE
                                    ---------


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                UNISYS CORPORATION


Date: December 20, 2000         By:  /s/Harold S. Barron
                                     ----------------------
                                     Harold S. Barron
                                     Senior Vice President and
                                     General Counsel

<PAGE>
 

                                  EXHIBIT INDEX
                                  -------------


Exhibit
No.

4     Amendment No. 2, dated as of December 7, 2000, to the Rights Agreement,
      dated as of March 7, 1986, between Unisys Corporation (then named
      Burroughs Corporation) and Harris Trust Company of New York, as Rights
      Agent, as amended on February 22, 1996, and as further amended on January
      10, 2000.





<PAGE>
 
Exhibit 4


                       AMENDMENT NO. 2 TO RIGHTS AGREEMENT

      AMENDMENT, dated as of December 7, 2000, to the Rights Agreement, dated as
of March 7, 1986 (the "Rights Agreement"), between Unisys Corporation, a
Delaware corporation (then named Burroughs Corporation) (the "Company"), and
Harris Trust Company of New York, as Rights Agent, as amended on February 22,
1996, and as further amended on January 10, 2000 to designate EquiServe Limited
Partnership and its subsidiary EquiServe Trust Company as Successor Rights Agent
(the "Rights Agent").

      Pursuant to Section 26 of the Rights Agreement, the Company and the Rights
Agent may from time to time supplement or amend the Rights Agreement in
accordance with the provisions of Section 26 thereof. All acts and things
necessary to make this Amendment a valid agreement, enforceable according to its
terms, have been done and performed, and the execution and delivery of this
Amendment by the Company and the Rights Agent have been in all respects duly
authorized by the Company and the Rights Agent.

      In consideration of the foregoing and the mutual agreements set forth
herein, the parties hereto agree as follows:

      1.  Subsection (a)(i) of Section 7 of the Rights Agreement shall be
deleted in its entirety
 and replaced with the following:

           (i)  the close of business on March 17, 2006 (the "Final
Expiration Date"), or

      2. This Amendment to the Rights Agreement shall be governed by and
construed in accordance with the laws of the State of Delaware and for all
purposes shall be governed by and construed in accordance with the laws of such
State applicable to contracts to be made and performed entirely within such
State.

      3. This Amendment to the Rights Agreement may be executed in any number of
counterparts and each of such counterparts shall for all purposes be deemed an
original and all such counterparts shall together constitute but one and the
same instrument. Terms not defined herein shall, unless the context otherwise
requires, have the meanings assigned to such terms in the Rights Agreement.

      4. Except as expressly set forth herein, this Amendment to the Rights
Agreement shall not by implication or otherwise alter, modify, amend or in any
way affect any of the terms, conditions, obligations, covenants or agreements
contained in the Rights Agreement, all of which are ratified and affirmed in all
respects and shall continue in full force and effect.

      5. If any term, provision, covenant or restriction of this Amendment to
the Rights Agreement is held by a court of competent jurisdiction or other
authority to be invalid, void or unenforceable, the remainder of the terms,
provisions, covenants and restrictions of this Amendment to the Rights
Agreement, and of the Rights Agreement, shall remain in full force and effect
and shall in no way be affected, impaired or invalidated.

<PAGE>
 
      IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed and attested, all as of the date and year first above written.

Attest:                             Unisys Corporation

By:   /s/ Susan T. Keene               By: /s/ Nancy Straus Sundheim
      ------------------                   --------------------------
                                           Nancy Straus Sundheim
                                           Vice President, Deputy General
                                           Counsel and Secretary

Attest:                             EquiServe Trust Company, N.A.


By:   /s/ Thomas A. Ferrari            By: /s/ M.J. Foley
      -------------------------            ----------------------------
                                           M.J. Foley
                                           Chief Business Development Officer

Attest:                             EquiServe Limited Partnership

By:   /s/ Thomas A. Ferrari                By: /s/ Robbin A. Mayo
      --------------------------           -----------------------------
                                           Robbin A. Mayo
                                           Senior Account Manager