  In the little Higgs model with T-parity (LHTM), the only tree-level
kinematically allowed two-body decay of the Z_H boson is Z_H-> A_H H and thus
one-loop induced two-body decays may have a significant rate. We study the
Z_H-> \gamma A_H decay, which is induced at the one-loop level by a fermion
triangle and is interesting as it depends on the mechanism of anomaly
cancellation of the model. All the relevant two- and three-body decays of the
Z_H gauge boson arising at the tree-level are also calculated. We consider a
small region of the parameter space where the scale of the symmetry breaking f
is still allowed to be as low as 500 GeV by electroweak precision data. We
first analyze the scenario of a Higgs boson with a mass of 120 GeV. We found
that the Z_H->\gamma A_H branching ratio can be of the order of a tree-level
three-body decay and may be at the reach of detection at the LHC for f close to
500 GeV, but it may be difficult to detect for f=1 TeV. There is also an
scenario where the Higgs boson has an intermediate mass such that the Z_H-> A_H
H decay is closed, the Z_H-> \gamma A_H gets considerably enhanced and the
chances of detection get a large boost.
