  In the scenario of gauge-Higgs unification, the origin of the Higgs boson is
higher dimensional gauge boson. Reflecting its origin, very characteristic
predictions are made of the Higgs boson interactions in this scenario.
Especially, a remarkable claim has been made: the contribution of non-zero
Kaluza-Klein modes to the Higgs decay $H \to Z \gamma$ exactly vanishes in the
minimal SU(3) electro-weak unified model, at least at the one-loop level. In
this brief report, in order to see whether this prediction is a general feature
of the scenario or the consequence of the specific choice of the model, matter
content or the order of perturbative expansion, we perform an operator
analysis. We demonstrate that there does not exist any relevant operator,
respecting the gauge symmetry SU(3) in the bulk. We also comment on the
possibly important contribution to the photonic decay $H \to \gamma \gamma$ due
to the non-zero Kaluza-Klein modes of light quarks.
