Two decay channels h →γγ , Zγ of the Standard Model–like Higgsin a left-rightsymmetry model are investigated using recent experimental data. We show that there exist one-loop contributions that affect the h → Zγ amplitude, but not the h → γγ amplitude. From numerical investigations, we show that the signal strength μZγ of the decay h → Zγ is still constrained strictly by that of h → γγ , namely |μγγ | < 38% results in maximum |μZγ | < 46%. On the other hand, the future experimental sensitivity |μγγ | = 4% still allows |μZγ | to reach values larger than the expected sensitivity of |μZγ | = 23%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .