We construct a simple model of fermion masses based on a spontaneously broken
S3×Z3 flavour group. At the leading order, in the neutrino sector
S3 is broken down to a
νμ–ντ parity subgroup that enforces a maximal atmospheric mixing angle and a vanishing
θ13. In the charged lepton sector the
νμ–ντ 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
and
,
λc 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.