  We propose a Grand Unified Theory of Flavour, based on $SO(10)$ together with
a non-Abelian discrete group $S_4$, under which the unified three quark and
lepton 16-plets are unified into a single triplet $3'$. The model involves a
further discrete group $ \mathbb{Z}_4^R\times \mathbb{Z}_4^3$ which controls
the Higgs and flavon symmetry breaking sectors. The CSD2 flavon vacuum
alignment is discussed, along with the GUT breaking potential and the
doublet-triplet splitting, and proton decay is shown to be under control. The
Yukawa matrices are derived in detail, from renormalisable diagrams, and
neutrino masses emerge from the type I seesaw mechanism. A full numerical fit
is performed with 15 input parameters generating 19 presently constrained
observables, taking into account supersymmetry threshold corrections. The model
predicts a normal neutrino mass ordering with a CP oscillation phase of
$260^{\circ}$, an atmospheric angle in the first octant and neutrinoless double
beta decay with $m_{\beta \beta}= 11$ meV. We discuss $N_2$ leptogenesis, which
fixes the second right-handed neutrino mass to be $M_2\simeq 2\times 10^{11}$
GeV, in the natural range predicted by the model.
