CERTIFICATION PURSUANT TO SECTION 302 OF THE SARBANES-OXLEY ACT

I, Carter E. Anthony, certify that:

      1. I have reviewed this report on Form N-CSR of RMK High Income Fund, Inc.
         (the "Fund");

      2. Based  on my  knowledge,  this  report  does  not  contain  any  untrue
         statement of a material fact or omit to state a material fact necessary
         to make the statements made, in light of the circumstances  under which
         such  statements  were made, not misleading  with respect to the period
         covered by this report;

      3. Based on my knowledge,  the financial  statements,  and other financial
         information  included in this  report,  fairly  present in all material
         respects the financial condition, results of operations, changes in net
         assets,  and cash flows (if the  financial  statements  are required to
         include a  statement  of cash  flows) of the Fund as of,  and for,  the
         periods presented in this report;

      4. The  Fund's  other  certifying  officer(s)  and I are  responsible  for
         establishing  and  maintaining  disclosure  controls and procedures (as
         defined in Rule 30a-3(c) under the Investment  Company Act of 1940) and
         internal control over financial  reporting (as defined in Rule 30a-3(d)
         under the Investment Company Act of 1940) for the Fund and have:

            (a) Designed such disclosure controls and procedures, or caused such
            disclosure   controls  and  procedures  to  be  designed  under  our
            supervision,  to ensure that  material  information  relating to the
            Fund, including its consolidated  subsidiaries,  is made known to us
            by others within those entities,  particularly  during the period in
            which this report is being prepared;

            (b) [Omitted]

            (c) Evaluated the  effectiveness of the Fund's  disclosure  controls
            and  procedures and presented in this report our  conclusions  about
            the effectiveness of the disclosure controls and procedures, as of a
            date within 90 days prior to the filing date of this report based on
            such evaluation; and

            (d)  Disclosed  in this  report any  change in the  Fund's  internal
            control over  financial  reporting  that occurred  during the second
            fiscal  quarter  of the  period  covered  by this  report  that  has
            materially  affected,  or is reasonably likely to materially affect,
            the Fund's internal control over financial reporting; and

      5. The Fund's  other  certifying  officer(s)  and I have  disclosed to the
         Fund's  auditors  and  the  audit  committee  of the  Fund's  board  of
         directors (or persons performing the equivalent functions):

            (a) All  significant  deficiencies  and material  weaknesses  in the
            design or operation of internal  control  over  financial  reporting
            which are reasonably  likely to adversely  affect the Fund's ability
            to record, process, summarize, and report financial information; and




            (b) Any fraud, whether or not material,  that involves management or
            other  employees who have a significant  role in the Fund's internal
            control over financial reporting.




Date: June 2, 2004                              /s/ Carter E. Anthony
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                                                Carter E. Anthony, President