  We investigate neutrino masses and mixings within the framework of the Zee
mass matrix, with three lepton flavors. It is shown that the bi-maximal
solution is the only possibility to reconcile atmospheric and solar neutrino
data, within this ansatz. We obtain two almost degenerate neutrinos, which are
mixtures of all three neutrino flavors, with heavy masses $\simeq \sqrt{\Delta
m_{atm}^2}$. The predicted mass of the lightest neutrino, which should consist
mostly of $\nu_{\mu}$ and $\nu_{\tau}$, is $\simeq \Delta
m_{\odot}^2/(2\sqrt{\Delta m_{atm}^2})$.
