  In the present note, first we derive an intrinsic inequality for
Pseudo-umbilical spacelike submanifold in an indefinite space form. We use this
inequality to show that such submanifold is totally geodesic. In the rest part
of this paper, using a result of Aiyama [1], we prove that Pseudo-umbilical
spacelike subamnifold is totally umbilical.
