  We have calculated the width of the rare decay $H\to\gamma\gamma Z$ at
one-loop level in the standard model for Higgs boson masses in the range $115
{\rm GeV} \leq m_H \leq 160 {\rm GeV}$ . For this range of Higgs boson masses
we find that $Z$ boson is predominantly longitudinally polarized, and the
photons have the same helicity. A comparison of the decay width $\Gamma(H\to
\gamma\gamma Z)$ to those of $H\to\gamma\gamma$ and $H\to\gamma Z$ shows that,
for the Higgs boson mass of $m_H \sim 135 \rm{GeV}$, the ratios of the decay
widths are $\Gamma(H\to\gamma\gamma Z) / \Gamma(H\to\gamma\gamma) \sim
\Gamma(H\to\gamma\gamma Z) / \Gamma(H\to\gamma Z) \sim 10^{-5}-10^{-6}$.
