  The next-to-leading-order $O(1/Q^4)$ power correction for $\eta\gamma$ and
$\eta^\prime\gamma$ form factors are evaluated and employed to explore the
$\eta-\eta^\prime$ mixing. The parameters of the two mixing angle scheme are
extracted from the data for form factors, two photon decay widths and radiative
$J/\psi$ decays. The $\chi^2$ analysis gives the result:
$f_{\eta_1}=(1.16\pm0.06)f_\pi, f_{\eta_8}=(1.33\pm0.23)f_\pi,
\theta_1=-9^\circ\pm 3^\circ, \theta_8=-21.3^\circ\pm 2.3^\circ$, where
$f_{\eta_{1(8)}}$ and $\theta_{1(8)}$ are the decay constants and the mixing
angles for the singlet (octet) state. In addition, we arrive at a stringent
range for $f_{\eta^\prime}^c:-10$ MeV$\le f_{\eta^\prime}^c\le -4$ MeV.
