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^*\rightarrow B\gamma \gamma and D^*\rightarrow D\gamma \gamma . It is shown that the branching ratio of D^*\rightarrow 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 x 10^-6 and 3.3 x 10^-5 for 0.25 < g < 1.

PACS numbers: 12.39.Fe, 12.39.Hg, 13.25.--k, 13.40.Hq