  Intermediate hadronic meson loop contributions to $J/\psi$, $\psi^\prime \to
\gamma\eta_c$ ($\gamma\eta_c^\prime$) are studied apart from the dominant M1
transitions in an effective Lagrangian approach. Due to the property of the
unique antisymmetric tensor coupling in $V\to VP$, the hadronic loop
transitions provide explicit corrections to the M1 transition amplitudes
derived from the naive "quenched" $c\bar{c}$ transitions via the coupling form
factors. This mechanism interfering with the M1 transition amplitudes naturally
accounts for the deviations from the Godfrey-Isgur model predictions in
$J/\psi$ and $\psi^\prime\to \gamma\eta_c$. It also predicts a small branching
ratio of $\psi^\prime\to \gamma\eta_c^\prime$, which can be examined by
experimental measurements at BES and CLEO-c.
