  The exchange symmetry between the muon neutrino and the tau neutrino for the
neutrino mass matrix has been very useful in understanding the near maximal
atmospheric neutrino mixing angle. However, this symmetry can not be imposed at
the Lagrangian level, since the charged lepton partners, muon and tau do not
satisfy this symmetry. We extend the Standard model to include three right
handed singlet neutrinos, and impose the most general symmetry between
$\nu_{\mu R} $ and $\nu_{\tau R}$ sectors followed by a CP transformation of
the leptonic sector at the Lagrangian level. This symmetry does not affect the
charged leptons. With the additional assumption of the hermiticity of the
ensuing Dirac neutrino mass matrix, we get a 4 parameter neutrino mass matrix
in good agreement with the available neutrino data for the inverted neutrino
mass hierarchy. The model also predicts the values of the three neutrino
masses, and the leptonic CP violating phase which can be tested in the upcoming
neutrino experiments.
