  We construct a simple model of fermion masses based on a spontaneously broken
S3 X Z3 flavour group. At the leading order, in the neutrino sector S3 is
broken down to a \nu_\mu-\nu_\tau parity subgroup that enforces a maximal
atmospheric mixing angle and a vanishing \theta_{13}. In the charged lepton
sector the \nu_\mu-\nu_\tau parity is maximally broken and the resulting mass
matrix is nearly diagonal. The charged lepton mass hierarchy is automatically
reproduced by the S3 symmetry breaking parameter alone. A careful analysis
shows that, after the inclusion of all relevant subleading effects, the model
predicts \theta_{23}=\pi/4+O(\lambda_c^2) and \theta_{13}=O(\lambda_c^2),
\lambda_c denoting the Cabibbo angle. A simple extension to the quark sector is
also illustrated, where the mass spectrum and the mixing angles are naturally
reproduced, with the exception of the mixing angle between the first two
generations, that requires a small accidental enhancement.
