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 ${\mathbb{S}}_{4}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}$. Two standard model doublets, ${L}_{\ensuremath{\mu}}$ and ${L}_{\ensuremath{\tau}}$, are assigned simultaneously to a $\mathbf{2}$ representation of ${\mathbb{S}}_{4}$. When the scalar fields introduced in this model, in addition to the standard model Higgs, and the leptons are coupled within the symmetry, the seesaw mechanism results in the tribimaximal neutrino mixing. This study examined the possible deviations from tribimaximal mixing related to the experimental data.