Assuming lepton number conservation, hermiticity of the neutrino mass matrix and νμ–ντ 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, 9.16×10−2 eV , 9.21×10−2 eV and 7.80×10−2 eV , a large value for the CP violating phase, δ=109.63° , and of course, the absence of neutrinoless ββ decay. All of these predictions can be tested in the forthcoming or future precision neutrino experiments.