  Two decay channels $h\rightarrow \gamma \gamma, Z\gamma$ of the Standard
Model-like Higgs in a left-right symmetry model are investigated under recent
experimental data. We will show there exist one-loop contributions that affect
the $h\rightarrow Z\gamma$ amplitude, but not the $h\rightarrow \gamma\gamma$
amplitude. From numerical investigations, we show that the signal strength
$\mu_{Z \gamma}$ of the decay $h\rightarrow Z\gamma$ is still constrained
strictly by that of $h\rightarrow \gamma\gamma$, namely $|\Delta \mu_{\gamma
\gamma}|<38\%$ results in max $|\Delta \mu_{Z \gamma}|<46\%$. On the other
hand, the future experimental sensitivity $|\Delta \mu_{\gamma \gamma}|=4\%$
still allows $|\Delta \mu_{Z \gamma}|$ reaches to values larger than the
expected sensitivity $|\Delta \mu_{Z \gamma}|=23\%$.
