  Recent LHC experiments have revealed that Higgs is light. As an interesting
candidate to accommodate light Higgs, in this paper we adopt the scenario of
dimensional deconstruction, where Higgs is redarded as a pseudo-Nambu-Goldstone
boson. Though the scenario is formulated in ordinary 4-dimensional space-time,
it may also be interpreted as "latticized" gauge-Higgs unification. We point
out that in this scenario Higgs interaction with matter field is anomalous,
i.e. its coupling deviates from what the standard model predicts. The interplay
between the periodicity of physical observables in the Higgs field and the
violation of translational invariance along the extra-space due to the
latticization is argued to play an essential role to get the anomalous
interaction. Though the predicted anomalous Higgs interaction has much
similarity to the one in the gauge-Higgs unification, in the case of
dimensional deconstruction the anomaly exists even if we do not introduce bulk
mass term for the chiral fermion realized by orbifolding, in clear contrast to
the case of gauge-Higgs unification. It in turn means that the anomaly goes
away in the continuum limit of the extra-space.
