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                              UNITED BANCORP, INC.
                                 CERTIFICATIONS

                                                                    Exhibit 31.2

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

1.  I have reviewed this quarterly report on Form 10-Q of United Bancorp, 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 and 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 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 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) 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.  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: November 12, 2004         s/s Randall M. Greenwood
                                     -------------------------------------------
                                     Randall M. Greenwood, Senior Vice President
                                     and Chief Financial Officer