  We present a complete calculation of the contributions to the effective
leptonic weak mixing angle, sin^2theta_eff, generated by closed fermion loops
at the two-loop level of the electroweak interactions. This quantity is the
source of the most stringent bound on the mass, M_H, of the only undiscovered
particle of the Standard Model, the Higgs boson. The size of the corrections
with respect to known partial results varies between -4*10^-5 and -8*10^-5 for
a realistic range of M_H from 100 to 300 GeV. This translates into a shift of
the predicted (from sin^2theta_eff alone) central value of M_H by +19 GeV, to
be compared with the shift induced by a recent change in the measured top quark
mass which amounts to +36 GeV. Our result, together with all other known
corrections is given in the form of a precise fitting formula to be used in the
global fit to the electroweak data.
