The power law decay of the aftershocks rate is observed only after a characteristic time scale c. The dependence of c on the mainshock magnitude MM and on the lower cut‐off magnitude MI is well established. By considering ten sequences recorded in the California Catalog we show that the aftershock number distribution becomes independent of both MM and MI if time is rescaled by an appropriate time scale fixed by the difference MM − MI. This result is interpreted within a more general dynamical scaling hypothesis recently formulated, relating time differences to magnitude differences. The above hypothesis gives predictions in good agreement with the recent findings by Peng et al. (2007).