Washington, D.C. 20549

                                  SCHEDULE 13G

                                 (Rule 13d-102)


                   Under the Securities Exchange Act of 1934
                                (Amendment No. 2)

                                 HALLIBURTON CO
                                (Name of Issuer)

                                  Common Stock
                         (Title of Class of Securities)

                                 (CUSIP Number)

                               December 31, 2005
            (Date Of Event which Requires Filing of this Statement)

Check the following box if a fee is being paid with this statement [].

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*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the

CUSIP No. 406216101 13G Page 2 of 6 Pages - -------------------------------------------------------------------------------- 1. NAME OF REPORTING PERSON(S) S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON(S) Morgan Stanley IRS # 36-314-5972 - -------------------------------------------------------------------------------- 2. CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) [ ] (b) [ ] - -------------------------------------------------------------------------------- 3. SEC USE ONLY - -------------------------------------------------------------------------------- 4. CITIZENSHIP OR PLACE OF ORGANIZATION The state of organization is Delaware. - -------------------------------------------------------------------------------- NUMBER OF 5. SOLE VOTING POWER SHARES 4,671,447 BENEFICIALLY -------------------------------------------------------------- OWNED BY 6. SHARED VOTING POWER EACH 8,423 REPORTING -------------------------------------------------------------- PERSON 7. SOLE DISPOSITIVE POWER WITH 4,671,447 -------------------------------------------------------------- 8. SHARED DISPOSITIVE POWER 8,423 - -------------------------------------------------------------------------------- 9. AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 4,799,801 - -------------------------------------------------------------------------------- 10. CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES* - -------------------------------------------------------------------------------- 11. PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9) 0.9% - -------------------------------------------------------------------------------- 12. TYPE OF REPORTING PERSON* IA, CO, HC - -------------------------------------------------------------------------------- *SEE INSTRUCTIONS BEFORE FILLING OUT!

CUSIP No. 406216101 13G Page 3 of 6 Pages Item 1. (a) Name of Issuer: HALLIBURTON CO -------------------------------------------------------------- (b) Address of Issuer's Principal Executive Offices: 1401 MCKINNEY HOUSTON, TX 77010 -------------------------------------------------------------- Item 2. (a) Name of Person Filing: Morgan Stanley -------------------------------------------------------------- (b) Address of Principal Business Office, or if None, Residence: 1585 Broadway New York, NY 10036 -------------------------------------------------------------- (c) Citizenship: Incorporated by reference to Item 4 of the cover page pertaining to each reporting person. -------------------------------------------------------------- (d) Title of Class of Securities: Common Stock -------------------------------------------------------------- (e) CUSIP Number: 406216101 -------------------------------------------------------------- Item 3. Morgan Stanley is a parent holding company.

CUSIP No. 406216101 13-G Page 4 of 6 Pages Item 4. Ownership. Incorporated by reference to Items (5) - (9) and (11) of the cover page. (a) Morgan Stanley is filing solely in its capacity as the parent company of, and indirect beneficial owner of securities held by, one of its business units. Item 5. Ownership of Five Percent or Less of a Class. As of the date hereof, Morgan Stanley has ceased to be the beneficial owner of more than five percent of the class of securities. See item 4(a) Item 6. Ownership of More Than Five Percent on Behalf of Another Person. Inapplicable Item 7. Identification and Classification of the Subsidiary which Acquired the Security Being Reported on By the Parent Holding Company. Item 8. Identification and Classification of Members of the Group. Item 9. Notice of Dissolution of Group. Item 10. Certification. By signing below I certify that, to the best of my knowledge and belief, the securities referred to above were acquired in the ordinary course of business and were not acquired for the purpose of and do not have the effect of changing or influencing the control of the issuer of such securities and were not acquired in connection with or as a participant in any transaction having such purpose or effect.

CUSIP No. 406216101 13-G Page 5 of 6 Pages Signature. After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct. Date: February 15, 2006 Signature: /s/ Dennine Bullard ----------------------------------------------------------------- Name/Title Dennine Bullard/Executive Director, Morgan Stanley & Co. Incorporated ----------------------------------------------------------------- MORGAN STANLEY INDEX TO EXHIBITS PAGE ----------------- ---- EXHIBIT 1 Secretary's Certificate Authorizing Dennine Bullard 6 to Sign on behalf of Morgan Stanley * Attention. Intentional misstatements or omissions of fact constitute federal criminal violations (see 18 U.S.C. 1001).

EX-99.b SECRETARY'S CERTIFICATE CUSIP No. 406216101 13-G Page 6 of 6 Pages EXHIBIT 1 ------------------ MORGAN STANLEY SECRETARY'S CERTIFICATE I, Charlene R. Herzer, a duly elected and acting Assistant Secretary of Morgan Stanley, a corporation organized and existing under the laws of the State of Delaware (the "Corporation"), certify as follows: (1) Donald G. Kempf, Jr. served as the duly elected Executive Vice President, Chief Legal Officer and Secretary of the Corporation from December 1, 1999 to August 26, 2005; (2) Pursuant to Section 7.01 of the Bylaws of the Corporation and resolutions approved by the Board of Directors of the Corporation on September 25, 1998, the Chief Legal Officer is authorized to enter into agreements and other instruments on behalf of the Corporation and may delegate such powers to others under his jurisdiction; and (3) Donald G. Kempf signed a Delegation of Authority as of February 23, 2000, which authorized Dennine Bullard to sign reports to be filed under Section 13 and 16 of the Securities Exchange Act of 1934 on behalf of the Corporation. Such authorization is in full force and effect as of this date. IN WITNESS WHEREOF, I have hereunto set my name and affixed the seal of the Corporation as of the 23rd day of January, 2006. ______________________________ Charlene R. Herzer Assistant Secretary