  In view of the fact that the data on neutrino mixing are still compatible
with a situation where Bimaximal mixing is valid in first approximation and it
is then corrected by terms of order of the Cabibbo angle, arising from the
diagonalization of the charged lepton masses, we construct a model based on the
discrete group S4 where those properties are naturally realized. The model is
supersymmetric in 4-dimensions and the complete flavour group is S4 x Z4 x
U(1)_FN, which also allows to reproduce the hierarchy of the charged lepton
spectrum. The only fine tuning needed in the model is to reproduce the small
observed value of r, the ratio between the neutrino mass squared differences.
Once the relevant parameters are set to accommodate r then the spectrum of
light neutrinos shows a moderate normal hierarchy and is compatible, within
large ambiguities, with the constraints from leptogenesis as an explanation of
the baryon asymmetry in the Universe.
