  An analysis of the leptonic texture for the new triangular mass matrices has
been carried out. In particular, it is shown that both bimaximal and nearly
bimaximal solutions for solar and atmospheric neutrino anomalies can be
generated within this pattern. We have also derived exact and compact
parametrization of the leptonic mixing matrix in terms of the lepton masses and
the parameters $\alpha, \beta'$ and $\delta$. A consistency with the CHOOZ
reactor result for $V_m{_{13}}$ and a smallness of the Jarlskog's invariant
parameter are obtained.
