  We find the effective neutral current in the heavy top quark limit up to and
including the terms of order $\alpha_s^3$. The result is then employed to
compute the correction of the same order to the axial part of the Z decay rate
into hadrons ($\G^h_Z$) induced by the top-bottom quark mass splitting. The
calculations confirm the prediction made in a previous work of K.G.Ch. and
J.H.K\"uhn (Phys. Lett. B 308 (1993) 127), namely, the effect of the singlet
corrections of order $\alpha^3_s$ to the axial part of the $\G^h_Z$ should not
exceed 25\% - 30\% (depending on the values chosen for $\alpha_s(M_Z)$ and
$m_t$) of the magnitude of the leading (singlet) $\alpha_s^2$ term.
