  Let $M^4$ be a closed immersed minimal hypersurface with constant squared
length of the second fundamental form $S$ and constant 3-mean curvature $H_3$
in $\mathbb{S}^{5}$. If $H_3^2\leq \frac{1}{2}.$ and Gauss-Kronecker curvature
$K_M$ satisfies $K_M\leq1$ $($or $ K_M\leq\frac{S^2}{144}$$)$, then $M^4$ is
isoparametric.
