For the vertex corrections to the partial decay rate
$\Gamma(Z\to b\bar{b})$ involving the top quark only the leading terms
of order $\alpha\alpha_s$ in the $1/M_t$ expansion are known. In this
work we compute the missing next-to-leading corrections. They turn out
to be equally important as the leading term and therefore have to be
included into an ${\cal O}(\alpha\alpha_s)$ analysis to arrive at
reliable predictions.