  It is interesting to investigate the OZI-forbidden radiative orthoquarkonium
decays $J/\psi\to \gamma\pi^0, \gamma\eta$ and $\gamma\eta'$ in perturbative
QCD. In this work without the approximations adopted in literature we carry out
a full one-loop calculation which involves integrations of 4-point and 5-point
loop functions. Our numerical results are in agreement with the present data.
We also briefly discuss the decays of $J/\psi\to \gamma+\rho^0$, as well as
$\Upsilon\to \pi^0\gamma, \eta\gamma, \eta'\gamma$.
