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                                                                    EXHIBIT 31.2

                                 CERTIFICATIONS

I, Randall M. Greenwood, Chief Financial Officer of United Bancorp, Inc.,
certify that:

6.       I have reviewed this annual report on Form 10-K of United Bancorp,
         Inc.;

7.       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;

8.       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 and cash flows
         of the registrant as of, and for, the periods presented in this report;

9.       The registrant's other certifying officer(s) and I are 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:

         (e) 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;

         (f) [THIS PARAGRAPH INTENTIONALLY LEFT BLANK.]

         (g) 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

         (h) 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

10.      The registrant's other certifying officer(s) and 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: March 29, 2004                    /s/ Randall M. Greenwood
                                                 -------------------------
                                                 Randall M. Greenwood, CFO