  We propose a generalized $\mu-\tau$ reflection symmetry to constrain the
lepton flavor mixing parameters. We obtain a new correlation between the
atmospheric mixing angle $\theta_{23}$ and the "Dirac" CP violation phase
$\delta_{\rm CP}$. Only in a specific limit our proposed CP transformation
reduces to standard $\mu-\tau$ reflection, for which $\theta_{23}$ and
$\delta_{CP}$ are both maximal. The "Majorana" phases are predicted to lie at
their CP-conserving values with important implications for the neutrinoless
double beta decay rates. We also study the phenomenological implications of our
scheme for present and future neutrino oscillation experiments including T2K,
NO$\nu$A and DUNE.
