  In this note, we generalize a characterization of the Clifford torus due to
Ros. Let $f:M\rightarrow S^{n+1}$ be an embedded closed minimal hypersurface.
Assume there are $(n+2)$ great hyperspheres of $S^{n+1}$ perpendicular to each
other, such that $M$ is symmetric with respect to them. Let $S$ denote the
square of the length of the second fundamental form of $f$ and let $\bar
S=\frac{1}{Vol(M)}\int_{M} Sd M$ be the average of $S$. Then $\bar S\geq n$
with equality holding if and only if $f$ is the Clifford torus $C_{m,n-m}$. It
can be rewritten as a Simons' type theorem: If $0\leq \int_M (n-S)d M$, then
either $S\equiv0$ or $S\equiv n$. This answers partially a conjecture by
Perdomo. Moreover, the estimate of the Willmore energy of $f$ is built:
$W(M)\geq n^{\frac{n}{2}}Vol(M)$.
