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 October 31, 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 Municipal High Income Fund Inc. /s/ R. Jay Gerken R. Jay Gerken Date: January 7, 2005	Chief Financial Officer Municipal High Income Fund Inc.Fund Inc. /s/ Kaprel Ozsolak Kaprel Ozsolak Date: January 7, 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.