  A complete study on the fermion masses and flavor mixing is presented in a
non-minimal left-right symmetric model (NMLRMS) where the ${\bf S}_{3}\otimes
{\bf Z}_{2}\otimes {\bf Z}^{e}_{2}$ flavor symmetry drives the Yukawa
couplings. In the quark sector, the mass matrices possess a kind of the
generalized Fritzsch textures that allow us to fit the CKM mixing matrix in
good agreement to the last experimental data. In the lepton sector, on the
other hand, a soft breaking of the $\mu\leftrightarrow \tau$ symmetry provides
a non zero and non maximal reactor and atmospheric angles, respectively. The
inverted and degenerate hierarchy are favored in the model where a set of free
parameters is found to be consistent with the current neutrino data.
