  The $O(\alpha m_t^2/m_w^2)$ and $O(\alpha \alpha_s m_t^2/m_w^2)$ corrections
to the partial decay width $\Gamma(Z \rightarrow b + \bar{b})$ are computed
using the current algebra formulation of radiative corrections. This framework
allows one to easily enforce the relevant Ward identity that greatly simplifies
the calculations. As a result, the one-loop $O(\alpha m_t^2/m_w^2)$
contribution is computed through the investigation of only two convergent
diagrams. The computation of the QCD corrections to the one-loop $O(\alpha
m_t^2/m_w^2)$ term involves fewer diagrams than in the standard approach. In
particular, the number of infrared divergent contribution is reduced. The
calculation is performed in the dimensional regularization scheme and no term
more divergent than $\frac{1}{n-4}$ is found. Our result confirms the screening
of the one-loop top mass effect recently found by Fleischer {\em et al.}.
