UNITED STATES
                       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)             September 30, 2004
_______________________________________________________________________________

                               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)


Check the appropriate box below if the Form 8-K filing is intended to
simultaneously satisfy the filing obligation of the registrant under any of
the following provisions (see General Instruction A.2. below):

\ \  Written communications pursuant to Rule 425 under the Securities Act
     (17 CFR 230.425)

\ \  Soliciting material pursuant to Rule 14a-12 under the Exchange Act
     (17 CFR 240.14a-12)

\ \  Pre-commencement communications pursuant to Rule 14d-2(b) under the
     Exchange Act (17 CFR 240.14d-2(b)

\ \  Pre-commencement communications pursuant to Rule 13e-4(c) under the
     Exchange Act (17 CFR 240.13e-4(c))



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ITEM 2.02.  RESULTS OF OPERATIONS AND FINANCIAL CONDITION.

On October 6, 2004, Unisys Corporation issued a news release regarding a tax
refund and a third quarter 2004 charge for actions to reduce administrative
expenses.  The release is furnished as Exhibit 99 to this Current Report.

The information in this Item 2.02 and in Exhibit 99 shall not be deemed to be
"filed" for purposes of Section 18 of the Securities Exchange Act of 1934, as
amended, or otherwise subject to the liabilities of that section.  The
information contained in this Item 2.02 and in Exhibit 99 shall not be
incorporated into any registration statement or other document filed with the
Securities and Exchange Commission by the company, whether made before or after
the date hereof, regardless of any general incorporation language in such
filing, except as shall be expressly set forth by specific reference in such
filing.

ITEM 2.05.  COSTS ASSOCIATED WITH EXIT OR DISPOSAL ACTIVITIES.

As part of its ongoing efforts to reduce its cost base and enhance its
administrative efficiency, on September 30, 2004, the company consolidated
facility space and committed to a reduction in global headcount of about 1400
employees, primarily in general and administrative areas.  These actions, which
are expected to be substantially completed by the end of the second quarter of
2005, will result in a one-time after-tax charge to earnings of approximately
$63 million (approximately $5 million for facility consolidations and
approximately $58 million for headcount reductions) in the third quarter of
2004.  The company anticipates cash requirements for these actions of
approximately $85 million, mostly in 2005.

ITEM 8.01.  OTHER EVENTS.

The U.S. Congressional Joint Committee on Taxation has approved an income tax
refund to the company related to the settlement of tax audit issues dating from
the mid-1980s.  The refund, including interest, is approximately $40 million.
After payment of related state taxes, the company expects a net cash refund of
approximately $30 million by the end of 2004 or in early 2005.  As a result of
the resolution of these audit issues, the company will be recording favorable
adjustments to its existing tax liability reserves, which will result in an
after-tax benefit of approximately $70 million to net income in the third
quarter of 2004.

ITEM 9.01.  FINANCIAL STATEMENTS AND EXHIBITS.

(c)  The following exhibit is being furnished herewith:

     99  News Release, dated October 6, 2004, of Unisys Corporation



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                                   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: October 6, 2004                             By: /s/Janet B. Haugen
                                                      -------------------
                                                      Janet B. Haugen
                                                      Senior Vice President and
                                                      Chief Financial Officer