  In this paper, we consider the problem of prescribing scalar curvature on
n-sphere. Assume that the candidate curvature function $f$, which is allowed to
change sign, satisfies some kind of Morse index or symmetry condition. By
studying the well-known scalar curvature flow, we are able to prove that the
flow converges to a metric with the prescribed function $f$ as its scalar
curvature.
