  The virtual effects of the Zee charged scalar boson on the
lepton-family-number (LFN) violating processes are studied. We obtain the
constraints on the individual Yukawa coupling constants of the Zee boson to
leptons. Using these constraints, we predict the upper bounds on the
muonium-antimuonium conversion probability, the branching fractions of the LFN
violating decays such as $\tau \to e\gamma$, $\tau \to \mu\gamma$, $\tau^- \to
\mu^+e^-e^-$ and $\tau \to e^+\mu^-\mu^-$. The contribution of the Zee boson to
the muon anomalous magnetic moment is also considered
