EXHIBIT 32.1

                            CERTIFICATION PURSUANT TO
            SECTION 1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to Section 1350, Chapter 63 of Title 18, United States Code, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, as
Acting Chief Executive Officer of The TJX Companies, Inc. (the "Company"), does
hereby certify that to my knowledge:

      1.    the Company's Annual Report on Form 10-K for the fiscal year ended
            January 28, 2006 fully complies with the requirements of Section
            13(a) or 15(d) of the Securities Exchange Act of 1934; and

      2.    the information contained in the Company's Annual Report on Form
            10-K for the fiscal year ended January 28, 2006 fairly presents, in
            all material respects, the financial condition and results of
            operations of the Company.


                               /s/ Bernard Cammarata
                               ----------------------------------------
                               Name:  Bernard Cammarata
                               Title: Acting Chief Executive Officer

Dated: March 29, 2006