  This work proposes a neutrino mass model that is derived using the minimal
seesaw mechanism which contains only two right-handed neutrinos, under the
non-abelian discrete flavor symmetry $\mathbb{S}_4\otimes\mathbb{Z}_2$. Two
standard model doublets, $L_\mu$ and $L_\tau$, are assigned simultaneously to a
$\mathbf{2}$ representation of $\mathbb{S}_4$. When the scalar fields
introduced in this model, addition to the Standard Model Higgs, and the leptons
are coupled within the symmetry, the seesaw mechanism results in the
tri-bi-maximal neutrino mixing. This study examined the possible deviations
from TBM mixing related to the experimental data.
