  In this paper, we prove that, up to similarity, there are only two minimal
hypersurfaces in $\mathbb{R}^{n+2}$ that are asymptotic to a Simons cone, i.e.
the minimal cone over the minimal hypersurface $\sqrt{\frac
pn}\mathbb{S}^p\times \sqrt{\frac{n-p}n} \mathbb{S}^{n-p}$ of
$\mathbb{S}^{n+1}$
