  We apply perturbative QCD to the radiative decays of charmonia $J/\psi$ and
$\chi_{cJ}$ into light mesons. We perform a complete numerical calculation for
the quark-gluon loop diagrams involved in these processes. The calculated
$J/\psi$ decay branching ratios to P-wave mesons $f_2(1270)$ and $f_1(1285)$
fit the data well, while that of $f_0(980)$ (if treated as an $s\bar s$ meson)
is predicted to be $1.6\times 10^{-4}$, which implies that $f_0(1710)$ can not
be the $s\bar s$ or $(u\bar u+d\bar d)/\sqrt{2}$ meson. Decays of P-wave
charmonia $\chi_{cJ}\to \rho(\omega, \phi)\gamma$ (J=0,1,2) are also studied,
and the branching ratio of $\chi_{c1}\to \rho\gamma$ is predicted to be
$1.4\times 10^{-5}$, which may be tested by CLEO-c and BESIII with future
experiments.
