  In this paper, we discuss the UV sensitivity of the Higgs effective potential
in a Gauge-Higgs Unification (GHU) model. We consider an $SU(\mathcal N)$ GHU
on $\mathbf M^4\times S^1$ spacetime with a massless Dirac fermion. In this
model, we evaluate the four-Fermi diagrams at the two-loop level and find them
to be logarithmically divergent in the dimensional regularization scheme.
Moreover, we confirm that their counter terms contribute to the Higgs effective
potential at the four-loop level. This result means that the Higgs effective
potential in the GHU depends on UV theories as well as in other
non-renormalizable theories.
