  We formulate general conditions on $3\times 3$ neutrino mass matrices under
which a degenerate pair of neutrinos at a high scale would split at low scale
by radiative corrections involving only the standard model fields. This
generalizes the original observations of Wolfenstein on pseudo Dirac neutrinos
to three generations. A specific model involving partially broken discrete
symmetry and solving the solar and atmospheric anomalies is proposed. The
symmetry pattern of the model naturally generates two large angles one of which
can account for the large angle MSW solution to the solar neutrino problem.
