  We consider a complete biharmonic hypersurface with nowhere zero mean
curvature vector field $\phi:(M^m,g)\rightarrow (S^{m+1},h)$ in a sphere. If
the squared norm of the second fundamental form $B$ is bounded from above by m,
and $\int_M H^{- p }dv_g<\infty$, for some $0<p<\infty$, then the mean
curvature is constant.
