FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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1. Name and Address of Reporting Person * BATTERSBY SCOTT A   2. Issuer Name and Ticker or Trading Symbol UNISYS CORP [UIS] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) Vice President and Treasurer (Last) (First) (Middle) UNISYS WAY 3. Date of Earliest Transaction (Month/Day/Year) 05/07/2010 (Street) BLUE BELL, PA 19424-0001 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Stock 05/07/2010   M   440 A $ 6.4 1,743.8 D   Common Stock               760.777 I by USP Trust

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Stock Option (right to buy)

$ 6.4

05/07/2010

M

440

(1)

02/12/2014

Common Stock

440

$ 0

7,560 (2)

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
BATTERSBY SCOTT A UNISYS WAY BLUE BELL, PA 19424-0001			Vice President and Treasurer

Signatures

By: Susan T. Keene, attorney-in-fact For: Scott A. Battersby		05/07/2010
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	Stock option granted under the terms and provisions of the Unisys Corporation 2007 Long-Term Incentive and Equity Compensation Plan. The stock option vests 50% on February 12, 2010, 25% on February 12, 2011 and 25% on February 12, 2012.
(2)	Includes previously granted stock options that have been adjusted to reflect a one-for-ten reverse stock split of the Issuer's common stock effected at 11:59 p.m. on October 23, 2009. Pursuant to the exemption under Rule 16a-9(a) of the Securities Exchange Act of 1934, these adjustment transactions are not required to be reported.

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