  We analytically compute the flavour singlet ${\cal O}(\alpha_s^2
m_b^2/m_t^2)$ radiative corrections to the partial decay rate
$\Gamma(Z\rightarrow b\bar{b})$. These corrections arise from anomalous
``double traingle'' diagrams containing a single $\gamma_5$ matrix inside each
of two closed fermion loops. They represent the next-to-leading term of the
asymptotic expansion in the inverse large top mass. As a byproduct of the
calculcation we confirm the results of B.Kniehl and J.H.K\"uhn for the flavour
singlet massless corrections \cite{KniKue90} as well as our previous ${\cal
O}(\alpha_s^2 m_b^2/M_Z^2)$ result \cite{CheKwi93}.
