  The PMNS neutrino mixing matrix is given, in general, by the product of two
unitary matrices associated with the diagonalization of the charged lepton and
neutrino mass matrices, respectively. Assuming that the active flavor neutrinos
possess a Majorana mass matrix which is diagonalized by a bimaximal mixing
matrix, we give the allowed forms of the charged lepton mixing matrix and the
corresponding implied forms of the charged lepton mass matrix. We further
assume that the origin of bimaximal mixing is a weakly broken flavor symmetry
of the neutrino Majorana mass matrix, corresponding to the conservation of the
non-standard lepton charge L' = L_e - L_mu - L_tau. The latter does not
predict, in general, the atmospheric neutrino mixing to be maximal. We study
the impact of this fact on the allowed forms of the charged lepton mixing
matrix and on the neutrino mixing observables, analyzing the case of CP
nonconservation in detail. We find, in particular, that the allowed ranges of
U_{e3} and of the atmospheric neutrino mixing angle are typically larger when
one assumes L' conservation than in the case of exact initial bimaximal mixing.
The atmospheric neutrino mixing can take any value inside its currently allowed
range, while |U_{e3}|^2 can be as small as 0.007. We discuss under which
conditions the atmospheric neutrino mixing angle can be larger or smaller than
pi/4. We present also a simple see-saw realization of the implied light
neutrino Majorana mass matrix and consider leptogenesis in this scenario.
