  The principle of maximum conformality (PMC) provides a convenient way for
setting the optimal renormalization scales for high-energy processes, which can
eliminate the conventional renormalization scale error via an order-by-order
manner. At present, we make a detailed PMC analysis on the Higgs decay
$H\rightarrow \gamma\gamma$ up to three-loop QCD corrections. As an important
point of deriving reliable PMC estimation, it is noted that only those
$\{\beta_i\}$-terms that rightly determine the running behavior of coupling
constant via the renormalization group equation should be absorbed into the
coupling constant, and those $\{\beta_i\}$-terms that pertain to the quark mass
renormalization and etc. should be kept as a separate. To avoid confusion of
separating and absorbing different types of $\{\beta_i\}$-terms into the
coupling constant, we first transform the decay width in terms of top quark
$\overline{\rm MS}$ mass into that of on-shell mass and then apply the PMC
scale setting. After applying PMC scale setting, the final estimation is
conformal and is scheme-independent and scale-independent. Up to three-loop QCD
corrections, we obtain a PMC scale $\mu^{\rm PMC}_{r}=242.3$ GeV $\sim 2M_H$,
which is optimal and highly independent of any choice of initial scale. Thus,
we obtain a more accurate scale-independent prediction by taking the Higgs mass
as the same as that of ATLAS and CMS measurements, i.e., $\Gamma(H\rightarrow
\gamma\gamma)|_{\rm ATLAS}=9.504^{+0.226}_{-0.252}$ keV and
$\Gamma(H\rightarrow \gamma\gamma)|_{\rm CMS}=9.568^{+0.195}_{-0.191}$ keV,
where the error is caused by the measured Higgs mass, i.e. the Higgs mass
$M_{H}$ is taken as $125.5\pm0.2^{+0.5}_{-0.6}$ GeV for ATLAS and
$125.7\pm0.3\pm0.3$ GeV for CMS, respectively.
