  The two-loop electroweak corrections to the anomalous magnetic moment of the
muon, generated by fermionic loops, are calculated. An interesting role of the
top quark in the anomaly cancellation is observed. New corrections, including
terms of order $G_\mu \alpha m_t^2$, are computed and a class of diagrams
previously thought to vanish are found to be important. The total fermionic
correction is $-(23\pm 3) \times 10^{-11}$ which decreases the electroweak
effects on $g-2$, predicted from one-loop calculations, by 12\%. We give an
updated theoretical prediction for $g-2$ of the muon.
