  Recent works related to Palis conjecture of J. Yang, S. Crovisier, M.
Sambarino and D. Yang showed that any aperiodic class of a $C^1$-generic
diffeomorphism far away from homoclinic bifurcations (or homoclinic tangencies)
is partially hyperbolic. We show in this paper that, generically, a non-trivial
dominated splitting implies partial hyperbolicity for an aperiodic class if it
is Lyapunov stable. More precisely, for $C^1$-generic diffeomorphisms, if a
Lyapunov stable aperiodic class has a non-trivial dominated splitting $E\oplus
F$, then one of the two bundles is hyperbolic (either $E$ is contracted or $F$
is expanded).
