  We present the two-loop ${\cal O}(\alpha_sG_Fm_t^2)$ correction to the $b\bar
b$ decay rate of the Stan\-dard-Model Higgs boson, assuming that the $t$ quark
is much heavier than the Higgs boson. Apart from the universal correction
connected with the renormalizations of the wave function and the vacuum
expectation value of the Higgs field, this involves vertex corrections specific
to the presence of beauty in the final state. We calculate the latter by means
of a low-energy theorem. All would-be mass singularities related to the $b$
quark can be absorbed into the running Higgs-bottom Yukawa coupling. It turns
out that the total ${\cal O}(\alpha_sG_Fm_t^2)$ correction screens the leading
high-$m_t$ behaviour of the one-loop result by 71\% to 75\% for $M_H$ between
60~GeV and $2M_W$.
