Exhibit (32)a

                    Certification of Chief Executive Officer
  Pursuant to Section 1350 of Chapter 63 of Title 18 of the United States Code

I, Thomas J. Falk, Chief Executive Officer of Kimberly-Clark Corporation,
certify that, to my knowledge:

(1)    the Form 10-Q, filed with the Securities and Exchange Commission on
       November 6, 2003 ("accompanied report") 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 accompanied report fairly presents, in
       all material respects, the financial condition and results of operations
       of Kimberly-Clark Corporation.




                                             /s/ Thomas J. Falk
                                             ------------------
                                             Thomas J. Falk
                                             Chief Executive Officer
                                             November 6, 2003