  We present a supersymmetric see-saw $S_4$ model giving rise to the most
general neutrino mass matrix compatible with Tri-Bimaximal mixing. We adopt the
$S_4\times Z_5$ flavour symmetry, broken by suitable vacuum expectation values
of a small number of flavon fields. We show that the vacuum alignment is a
natural solution of the most general superpotential allowed by the flavour
symmetry, without introducing any soft breaking terms. In the charged lepton
sector, mass hierarchies are controlled by the spontaneous breaking of the
flavour symmetry caused by the vevs of one doublet and one triplet flavon
fields instead of using the Froggatt-Nielsen U(1) mechanism. The next to
leading order corrections to both charged lepton mass matrix and flavon vevs
generate corrections to the mixing angles as large as ${\cal O}(\lambda_C^2)$.
Applied to the quark sector, the symmetry group $S_4\times Z_5$ can give a
leading order $V_{CKM}$ proportional to the identity as well as a matrix with
${\cal O}(1)$ coefficients in the Cabibbo $2\times 2$ submatrix. Higher order
corrections produce non vanishing entries in the other $V_{CKM}$ entries which
are generically of ${\cal O}(\lambda_C^2)$.
