  We study the texture two zeros neutrino mass matrices using the standard
parametrization for the neutrino mixing matrix. We find that if the origin of
CP violation in the leptonic sector is not due to the Dirac-type complex phase
of the mixing matrix but because of some non-standard phenomena then some of
the possible texture two mass matrices, which are allowed by standard
parametrization, are found to be unsuitable to accommodate the observed data in
the neutrino sector. Furthermore, incorporating nonzero Dirac phase in our
analysis we find that many of them do not exhibit normal hierarchy.
