  The strong g-coupling characterizes the interaction of heavy mesons with
pions in typical vertices $H^*H\pi$, $H^*H^*\pi$, where $(H^*;H)$ stands for
vector and pseudoscalar $(B^*;B)$ or $(D^*;D)$ heavy mesons. Its estimation by
different theoretical methods has led to a wide range of possible values. We
describe a new approach to the determination of g, which exploits the rare
radiative decays $B^*\to B\gamma\gamma$ and $D^*\to D\gamma\gamma$. It is shown
that the branching ratio of $D^*\to D\gamma\gamma$ can be expressed as a
function of a single unknown $g$ and we calculate it to be in the measurable
range between $1.6\times 10^{-6}$ and $3.3\times 10^{-5}$ for 0.25 < g < 1.
