  It was proposed recently by Murakami et al. [Science \textbf{301},
1348(2003)] that in a large class of $p$-doped semiconductors, an applied
electric field can drive a quantum dissipationless spin current in the
direction perpendicular to the electric field. In this paper we investigate the
effects of spin imbalance on this intrinsic $spin$ Hall effect. We show that in
a real sample with boundaries, due to the presence of spin imbalance near the
edges of the sample, the spin Hall conductivity is not a constant but a
sensitively $position$-$dependent$ quantity, and due to this fact, in order to
take the effects of spin imbalance properly into account, a microscopic
calculation of both the quantum dissipationless spin Hall current and the spin
accumulation on an equal footing is thus required. Based on such a microscopic
calculation, a detailed discussion of the effects of spin imbalance on the
intrinsic spin Hall effect in thin slabs of $p$-doped semiconductors are
presented.
