  We present the two-loop QED and QCD corrections to the $f\bar fH$ Yukawa
coupling that are induced by the exchange of a virtual photon or gluon,
respectively, with a heavy-fermion loop inserted. As an application, we study
the corresponding $\O(\alpha_s^2M_H^2/m_t^2)$ correction to the $H\to b\bar b$
decay rate.
