  We construct a Supersymmetric (SUSY) Grand Unified Theory (GUT) of Flavour
based on S4 x SU(5), together with an additional (global or local) Abelian
symmetry, and study it to next-to-leading order (NLO) accuracy. The model
includes a successful description of quark and lepton masses and mixing angles
at leading order (LO) incorporating the Gatto-Sartori-Tonin (GST) relation and
the Georgi-Jarlskog (GJ) relations. We study the vacuum alignment arising from
F-terms to NLO and such corrections are shown to have a negligible effect on
the results for fermion masses and mixings achieved at LO. Tri-bimaximal (TB)
mixing in the neutrino sector is predicted very accurately up to NLO
corrections of order 0.1%. Including charged lepton mixing corrections implies
small deviations from TB mixing described by a precise sum rule, accurately
maximal atmospheric mixing and a reactor mixing angle close to three degrees.
