CERTIFICATIONS PURSUANT TO SECTION 906
EX-99.906CERT

                                  CERTIFICATION

R. Jay Gerken, Chief Executive Officer, and Richard Peteka, Chief Financial
Officer of the Municipal High Income Fund Inc., 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, 2003 (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/ Richard Peteka
- -------------------------------              -----------------------------------
R. Jay Gerken                                Richard Peteka
Date: June 27, 2003                          Date: June 27, 2003

A signed original of this written statement required by Section 906, or other
document authenticating, acknowledging, or otherwise adopting the signature
that appears in typed form within the electronic version of this written
statement required by Section 906, has been provided to Municipal High Income
Fund Inc. and will be retained by Municipal High Income Fund Inc. and furnished
to the Securities and Exchange Commission or its staff upon request.

This certification is being furnished to the 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.