Exhibit 32.1

CERTIFICATION OF PERIODIC REPORT

I, J. Edward Coleman, Chairman of the Board 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, 2012 (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: November 1, 2012

/s/ J. Edward Coleman

J. Edward Coleman

Chairman of the Board 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.