<DOCUMENT>
<TYPE>EX-99.906
<SEQUENCE>3
<FILENAME>ex906.txt
<DESCRIPTION>CERTIFICATION UNDER SECTION 906
<TEXT>
CERTIFICATIONS PURSUANT TO SECTION 906
EX-99.906CERT

                                  CERTIFICATION

R. Jay Gerken, Chief Executive Officer, and Andrew B. Shoup, Chief
Administrative Officer of Municipal High Income Fund Inc. (the "Registrant"),
each certify to the best of his or her knowledge that:

      1. The Registrant's periodic report on Form N-CSR for the period ended
April 30, 2004 (the "Form N-CSR") fully complies with the requirements of
section 15(d) of the Securities Exchange Act of 1934, as amended; and

      2. The information contained in the Form N-CSR fairly presents, in all
material respects, the financial condition and results of operations of the
Registrant.


Chief Executive Officer                         Chief Administrative Officer
Municipal High Income Fund Inc.                 Municipal High Income Fund Inc.

/s/ R. Jay Gerken                               /s/ Andrew B. Shoup
-------------------------------                 -------------------------
R. Jay Gerken                                   Andrew B. Shoup
Date: July 6, 2004                              Date: July 6, 2004

This certification is being furnished to the Securities and Exchange Commission
solely pursuant to 18 U.S.C. ss. 1350 and is not being filed as part of the Form
N-CSR with the Commission.

</TEXT>
</DOCUMENT>
