  The $\pi^0 \gamma\gamma$ vertex for virtual photons of squared masses $q_1^2$
and $q_2^2$ plays a vital r\^ole in several physical processes; for example for
$q_1^2<0$, $q_2^2<0$, in the two-photon physics reaction $e^+ e^-\to e^+ e^-
\pi^0$, and for $q_1^2>0$, $q_2^2>0$, in the annihilation process $e^+ e^-\to
\pi^0 l^+ l^-$. It is also of interest because of its link to the axial
anomaly. We suggest a new approach to this problem. We have obtained a closed
analytic expression for the vertex in the limit in which at least one of
$|q_1^2|$ and $|q_2^2|$ is large for arbitrary fixed values of the ratio
$q_1^2/q_2^2$. We compare our results with those obtained previously by Brodsky
and Lepage. It should be straightforward to test our predictions
experimentally.
