  Current neutrino oscillation data indicate that the $3\times 3$
Pontecorvo-Maki-Nakagawa-Sakata matrix $U$ exhibits a $\mu$-$\tau$ flavor
interchange symmetry $|U^{}_{\mu i}| = |U^{}_{\tau i}|$ (for $i = 1, 2, 3$) as
a good approximation. In particular, the T2K measurement implies that the
maximal neutrino mixing angle $\theta^{}_{23}$ and the CP-violating phase
$\delta$ should be close to $\pi/4$ and $-\pi/2$, respectively. Behind these
observations lies a minimal flavor symmetry -- - the effective Majorana
neutrino mass term keeps invariant under the transformations $\nu^{}_{e \rm L}
\to (\nu^{}_{e \rm L})^c$, $\nu^{}_{\mu \rm L} \to (\nu^{}_{\tau \rm L})^c$ and
$\nu^{}_{\tau \rm L} \to (\nu^{}_{\mu \rm L})^c$. Extending this flavor
symmetry to the canonical seesaw mechanism, we find that the $R$-matrix
describing the strength of weak charged-current interactions of heavy Majorana
neutrinos satisfies $|R^{}_{\mu i}| = |R^{}_{\tau i}|$ as a consequence of
$|U^{}_{\mu i}| = |U^{}_{\tau i}|$. This result can be used to set a new upper
bound, which is about three orders of magnitude more stringent than before, on
the flavor mixing factor associated with the charged-lepton-flavor-violating
decay mode $\tau^- \to e^- + \gamma$.
