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                                                                    EXHIBIT 31.1


              CERTIFICATION OF CHIEF EXECUTIVE OFFICER, PURSUANT TO
                  SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002


      I, Timothy O'Malley, certify that:

1.    I have reviewed this report on Amendment No. 2 to Form 10-Q for Medwave,
      Inc. (the "Registrant");

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 and results of operations and cash flows
      of the Registrant as of, and for, the periods presented in this report;

4.    I am responsible for establishing and maintaining disclosure controls and
      procedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for
      the Registrant and have:

      (a)   Designed such disclosure controls and procedures, or caused such
            disclosure controls and procedures to be designed under my
            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)   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
            the end of the period covered by this report based on such
            evaluation; and

      (c)   Disclosed in this report any change in the Registrant's internal
            control over financial reporting that occurred during the
            Registrant's most recent fiscal quarter (the registrant's fourth
            fiscal quarter 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.    I have disclosed, based on our most recent evaluation of internal control
      over financial reporting, 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: February 22, 2005


                                     By:  /s/ Timothy J. O'Malley
                                          -------------------------------------
                                          Timothy J. O'Malley
                                          President and Chief Executive Officer
                                          (Principal Executive Officer and
                                          Principal Financial Officer)