**Exhibit
      31.2**





**CERTIFICATIONS**




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





1.
      I have
      reviewed 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 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)) and internal control over financial reporting (as
      defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) 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)  Designed
      such internal control over financial reporting, or caused such internal control
      over financial reporting to be designed under our supervision, to provide
      reasonable assurance regarding the reliability of financial reporting and the
      preparation of financial statements for external purposes in accordance with
      generally accepted accounting principles;





(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 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, 2008
            
            /s/Randall
                M. GreenwoodRandall
                M. Greenwood, CFO