  We construct two flavor models based on $S_4$ family symmetry and generalised
CP symmetry. In both models, the $S_4$ family symmetry is broken down to the
$Z^{SU}_2$ subgroup in the neutrino sector, as a consequence, the trimaximal
$\text{TM}_1$ lepton mixing is produced. Depending on the free parameters in
the flavon potential, the Dirac CP is predicted to be either conserved or
maximally broken, and the Majorana CP phases are trivial. The two models differ
in the neutrino sector. The flavon fields are involved in the Dirac mass terms
at leading order in the first model, and the neutrino mass matrix contains
three real parameters such that the absolute neutrino masses are fixed.
Nevertheless, the flavon fields enter into the Majorana mass terms at leading
order in the second model. The leading order lepton mixing is of the
tri-bimaximal form which is broken down to $\text{TM}_1$ by the next to leading
order contributions.
