  The partial decay rate of the $Z$ boson into bottom quarks constitutes an
important decay channel. This is mainly due to the virtual presence of the top
quark in the loop diagrams giving rise to correction factors which are
quadratic in the top quark mass. At one- and two-loop order it turned out that
the leading term in the heavy-top expansion leads to very good approximations
to the exact result. In this work the non-singlet diagrams at O(\alpha_s^2 G_F
M_t^2) are considered.
