  We compute the decay rate of the Standard Model Higgs boson to bottom quarks
to order $\alpha\alpha_s$. We apply the optical theorem and calculate the
imaginary part of three-loop corrections to the Higgs boson propagator using
asymptotic expansions in appropriately chosen mass ratios. The corrections of
order $\alpha\alpha_s$ are of the same order of magnitude as the ${\cal
O}(\alpha_s^3)$ QCD corrections but have the opposite sign.
