  We investigate the $O(\alpha_s v^2)$ correction to the process of
pseudoscalar quarkonium decay to two photons in nonrelativistic QCD (NRQCD)
factorization framework. The short-distance coefficient associated with the
relative-order $v^2$ NRQCD matrix element is determined to next-to-leading
order in $\alpha_s$ through the perturbative matching procedure. Some technical
subtleties encountered in calculating the ${O(\alpha_s)$ QCD amplitude are
thoroughly addressed.
