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The lepton flavor mixing matrix having one row or one column in common withthe bimaximal mixing up to permutations is still compatible with the presentneutrino oscillation data. We provide a thorough exploration of generating sucha mixing matrix from $S_4$ family symmetry and generalized CP symmetry$H_{CP}$. Supposing that $S_4\rtimes H_{CP}$ is broken down to$Z^{ST^2SU}_2\times H^{\nu}_{CP}$ in the neutrino sector and$Z^{TST^{2}U}_4\rtimes H^{l}_{CP}$ in the charged lepton sector, one column ofthe PMNS matrix would be of the form $\left(1/2, 1/\sqrt{2}, 1/2\right)^{T}$ upto permutations, both Dirac CP phase and Majorana CP phases are trivial inorder to accommodate the observed lepton mixing angles. The phenomenologicalimplications of the remnant symmetry $K^{(TST^2, T^2U)}_4\rtimes H^{\nu}_{CP}$in the neutrino sector and $Z^{SU}_{2}\times H^{l}_{CP}$ in the charged leptonsector are studied. One row of PMNS matrix is determined to be $\left(1/2, 1/2,-i/\sqrt{2}\right)$, and all the three leptonic CP phases can only be trivialto fit the measured values of the mixing angles. Two models based on $S_4$family symmetry and generalized CP are constructed to implement these modelindependent predictions enforced by remnant symmetry. The correct masshierarchy among the charged leptons is achieved. The vacuum alignment andhigher order corrections are discussed.

Deviation from Bimaximal Mixing and Leptonic CP Phases in $S_4$ Family Symmetry and Generalized CP