  The $\mu-\tau$ reflection symmetry of the lepton mixing matrix accommodates
maximal atmospheric mixing ($\theta_{23}=\pi/4$) as well as maximal Dirac CP
phase ($\delta=\pm \pi/2$) for the Dirac case. In the standard parametrization
of the PMNS matrix the reflection symmetric nature is not directly visible
while substituting the maximal values of the mixing parameters. This issue has
been addressed in this paper. It is found that the reflection symmetry in the
'standard' PMNS matrix can be restored by allowing maximal values of the
Majorana CP phases ($\alpha$, $\beta$) as well, along with maximal $\delta$. To
accommodate non-maximal values of $\theta_{23}$ and $\delta$ we consider
charged lepton contributions to the neutrino mixing and implement the proposed
scheme of reflection symmetry in the neutrino mixing matrix. The charged lepton
correction scheme succeeds in the prediction of lepton mixing parameters
consistent with the global $3\nu$ oscillation data.
