Corrections of $O(\alpha_s^2)$ to the decay of the top quark into a
W boson and a bottom quark are calculated. The method is based on an
expansion of the top quark propagator for small external momentum, q, as
compared to the top quark mass, M_t. The physical point q^2 = M_t^2 is
reached through Pad\'e approximations. The described method allows to
take effects induced by a finite W boson mass into account. The
numerical relevance of the result is discussed. Important cross-checks
against recent results for the decay rate $b \to u l \bar\nu$ and the
two-loop QED corrections to $\mu$-decay are performed.