  The neutrino mass matrix has remnant CP symmetry expressed in terms of the
lepton mixing matrix, and vice versa the remnant CP transformations allow us to
reconstruct the mixing matrix. We study the scenario that all the four remnant
CP transformations are preserved by the neutrino mass matrix. The most general
parameterization of remnant CP transformations is presented. The lepton mixing
matrix is completely fixed by the remnant CP, and its explicit form is derived.
The necessary and sufficient condition for conserved Dirac CP violating phase
is found. If the Klein four flavor symmetry generated by the postulated remnant
CP transformations arises from a finite flavor symmetry group, the
phenomenologically viable lepton flavor mixing would be the trimaximal pattern,
both Dirac CP phase $\delta_{CP}$ and Majorana phase $\alpha_{31}$ are either
$0$ or $\pi$ while another Majorana phase $\alpha_{21}$ is a rational multiple
of $\pi$. These general results are confirmed to be true in the case that the
finite flavor symmetry group is $\Delta(6n^2)$.
