  The zero mode of an extra-dimensional component of gauge potentials serves as
a 4D Higgs field in the gauge-Higgs unification. We examine QED on $M^4 \times
S^1$ and determine the mass and potential of a 4D Higgs field (the $A_5$
component) at the two loop level with gauge invariant reguralization. It is
seen that the mass is free from divergences and independent of the
renormalization scheme.
