  Using a recently proposed method arXiv:1910.11597 (Yu Meng et al.), we study
the two-photon decay rate of $\eta_c$ using two $N_f=2$ twisted mass gauge
ensembles with lattice spacings $0.067$fm and $0.085$fm. The results obtained
from these two ensembles can be extrapolated in a naive fashion to the
continuum limit, yielding a result that is consistent with the experimental one
within two standard deviations. To be specific, we obtain the results for
two-photon decay of $\eta_c$ as $\mathcal{B}(\eta_c\rightarrow 2\gamma)=
1.29(3)(18)\times 10^{-4}$ where the first error is statistical and the second
is our estimate for the systematic error caused by the finite lattice spacing.
It turns out that Ward identity for the vector current is of vital importance
within this new method. We find that the Ward identity is violated for local
current with a finite lattice spacing, however it will be restored after the
continuum limit is taken.
