  We simplify and extend our previous model for the masses and mixing matrix of
three Majorana neutrinos based on permutation symmetry $S_3$ and the
perturbations which violate this symmetry. The perturbations are arranged such
that we get the smaller solar neutrinos mass difference at second order. We
work out the corrections to the tribimaximal mixing matrix with the non-zero
value for $s_{13}$ and the conventional CP-violating phase. It is shown that
the results of the model are comparable with the global analysis of neutrino
oscillation data.
