  In a novel parametrization of neutrino mixing and in the approximation of
$\tau$-lepton dominance, we show that the one-loop renormalization-group
equations (RGEs) of Dirac neutrinos are different from those of Majorana
neutrinos even if two Majorana CP-violating phases vanish. As the latter can
keep vanishing from the electroweak scale to the typical seesaw scale, it makes
sense to distinguish between the RGE running effects of neutrino mixing
parameters in Dirac and Majorana cases. The differences are found to be quite
large in the minimal supersymmetric standard model with sizable $\tan\beta$,
provided the masses of three neutrinos are nearly degenerate or have an
inverted hierarchy.
