  In this note, we study Q-curvature flow on $S^4$ with indefinite
nonlinearity. Our result is that the prescribed Q-curvature problem on $S^4$
has a solution provided the prescribed Q-curvature $f$ has its positive part,
which possesses non-degenerate critical points such that $\Delta_{S^4} f\not=0$
at the saddle points and an extra condition such as a nontrivial degree
counting condition.
