We analytically compute the flavour singlet O(alpha(s)2m(b)2/m(t)2) radiative corrections to the partial decay rate GAMMA (Z --> bbBAR). These corrections arise from anomalous ''double triangle'' diagrams containing a single gamma5 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. Kuhn for the flavour singlet massless corrections [Phys Lett. B 224 (1990) 229; Nucl. Phys. B 329 (1990) 547] as well as our previous O(alpha(s)2m(b)2/M(Z)2) result [Phys. Lett. B 305 (1993) 285].