  Using a new estimate for the Peng-Terng invariant and the multiple-parameter
method, we verify a rigidity theorem on the stronger version of Chern
Conjecture for minimal hypersurfaces in spheres. More precisely, we prove that
if $M$ is a compact minimal hypersurface in $\mathbb{S}^{n+1}$ whose squared
length of the second fundamental form satisfies $0\leq S-n\leq\frac{n}{18}$,
then $S\equiv n$ and $M$ is a Clifford torus.
