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                              UNITED BANCORP, INC.
                                    EXHIBITS
                                                                    EXHIBIT 31.2

                                 CERTIFICATIONS

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

1.    I have reviewed this 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)   [THIS PARAGRAPH INTENTIONALLY LEFT BLANK.]

(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 the end of
      the period covered by 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 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: August 6, 2004         /s/ Randall M. Greenwood
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                             Randall M. Greenwood, Senior Vice President and CFO