Exhibit 32.1


                  CERTIFICATION OF PERIODIC REPORT

I, Lawrence A. Weinbach, Chairman, President and Chief Executive
Officer of Unisys Corporation (the "Company"), certify, pursuant to
Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350,
that:

(1)   the Quarterly Report on Form 10-Q of the Company for the quarterly
period ended September 30, 2003 (the "Report") fully complies with the
requirements of Section 13(a) of the Securities Exchange Act of 1934
(15 U.S.C. 78m); and

(2)   the information contained in the Report fairly presents, in all
material respects, the financial condition and results of operations of the
Company.


Dated: October 23, 2003



/s/ Lawrence A. Weinbach
- ------------------------
Lawrence A. Weinbach
Chairman, President and
Chief Executive Officer



A signed original of this written statement required by Section 906 has been
provided to the Company and will be retained by the Company and furnished to
the Securities and Exchange Commission or its staff upon request.