CERTIFICATIONS PURSUANT TO SECTION 906
EX-99.906CERT

CERTIFICATION

R. Jay Gerken, Chief Executive Officer, and Kaprel Ozsolak, Chief Financial 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, 2005 (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 Financial Officer
Municipal High Income Fund Inc.	Municipal High Income Fund Inc.
/s/ R. Jay Gerken	/s/ Kaprel Ozsolak
R. Jay Gerken	Kaprel Ozsolak
Date: July 8, 2005	Date: July 8, 2005

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