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.;

         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  registrant  as of, and for,  the  periods
                  presented in this report;

         4.       The  registrant'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) for the registrant 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  registrant,
                           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  registrant'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
                           registrant's    internal   control   over   financial
                           reporting that occurred during the registrant's  most
                           recent  fiscal  half-year  (the  registrant's  second
                           fiscal  half-year  in the case of an  annual  report)
                           that has materially affected, or is reasonably likely
                           to  materially  affect,  the  registrant's   internal
                           control over financial reporting; and

         5.       The  registrant's  other  certifying  officer(s)  and  I  have
                  disclosed to the registrant's auditors and the audit committee
                  of the registrant'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 registrant'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  registrant's   internal  control  over
                           financial reporting.




Date:    November 25, 2003           /s/ Carter E. Anthony
     ----------------------         ------------------------------------------
                                     Carter E. Anthony, President




         CERTIFICATION PURSUANT TO SECTION 302 OF THE SARBANES-OXLEY ACT

I, Joseph C. Weller, certify that:

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

         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  registrant  as of, and for,  the  periods
                  presented in this report;

         4.       The  registrant'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) for the registrant 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  registrant,
                           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  registrant'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
                           registrant's    internal   control   over   financial
                           reporting that occurred during the registrant's  most
                           recent  fiscal  half-year  (the  registrant's  second
                           fiscal  half-year  in the case of an  annual  report)
                           that has materially affected, or is reasonably likely
                           to  materially  affect,  the  registrant's   internal
                           control over financial reporting; and

         5.       The  registrant's  other  certifying  officer(s)  and  I  have
                  disclosed to the registrant's auditors and the audit committee
                  of the registrant'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 registrant'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  registrant's   internal  control  over
                           financial reporting.



Date:    November 25,  2003           /s/ Joseph C. Weller
     ----------------------         ------------------------------------------
                                     Joseph C. Weller, Treasurer