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 * GIBSON JOHN W JR   2. Issuer Name and Ticker or Trading Symbol HALLIBURTON CO [HAL] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner _____ Officer (give title below) __X__ Other (specify below) Former CEO Energy Ser Grp (Last) (First) (Middle) 4318 ORCHARD CHASE CT 3. Date of Earliest Transaction (Month/Day/Year) 12/30/2004 (Street) KATY, X1 77450 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 12/30/2004   M   119,970 (1) A (2) 155,885 D   Common Stock 12/30/2004   S   119,970 (3) D $ 39.21 155,885 D

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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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

Option to Buy Common Stock

$ 26.03

12/30/2004

M

32,940

01/02/2004

01/02/2014

Common Stock

32,940

$ 26.03

0 (4)

D

Option to Buy Common Stock

$ 26.875

12/30/2004

M

34,000

10/04/1996

10/04/2006

Common Stock

34,000

$ 26.875

0 (4)

D

Option to Buy Common Stock

$ 29.5625

12/30/2004

M

24,000

12/04/1996

12/04/2006

Common Stock

24,000

$ 29.5625

0 (4)

D

Option to Buy Common Stock

$ 28.125

12/30/2004

M

12,000

12/02/1998

12/02/2009

Common Stock

12,000

$ 28.125

0 (4)

D

Option to Buy Common Stock

$ 34.75

12/30/2004

M

39,000

12/06/2000

12/06/2010

Common Stock

39,000

$ 34.75

0 (4)

D

Option to Buy Common Stock

$ 31.55

12/30/2004

M

21,938

07/19/2001

07/19/2011

Common Stock

21,938

$ 31.55

0 (4)

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
GIBSON JOHN W JR 4318 ORCHARD CHASE CT KATY, X1 77450				Former CEO Energy Ser Grp

Signatures

John W. Gibson, Jr.		01/04/2005
**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)	Reporting person's employment and position as an officer was terminated as of December 2, 2004. Reporting person is filing this Form 4 voluntarily to report post-termination transactions. Filing person is not aware of any pre-termination matchable transactions. This number includes the aggregate of all employee stock options exercised on 12/30/2004.
(2)	Shares acquired at exercise prices of employee stock options ($26.875, $29.5625, $28.125, $34.75, $31.55)
(3)	Share were sold in a broker-assisted cashless exercise pursuant to procedures put in place by issuer.
(4)	Options expired for non-exercised underlying shares of common stock.

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