  Assuming lepton number conservation, hermiticity of the neutrino mass matrix
and $\nu_{\mu} - \nu_{\tau}$ exchange symmetry, we show that we can determine
the neutrino mass matrix completely from the existing data. Comparing with the
existing data, our model predicts an inverted mass hierarchy (close to a
degenerate pattern) with the three neutrino mass values, $8.91 \times 10^{-2}$
eV, $8.95 \times 10^{-2}$ eV, $7.50 \times 10^ {-2}$ eV, a large value for the
CP violating phase, $\delta = 110^0$, and of course, the absence of
neutrinoless $\beta \beta$ decay. All of these predictions can be tested in the
forthcoming or future precision neutrino experiments.
