  For each $n\geq 2$ we construct a new closed embedded mean curvature
self-shrinking hypersurface in $\mathbb{R}^{2n}$. These self-shrinkers are
diffeomorphic to $S^{n-1}\times S^{n-1}\times S^1$ and are $SO(n)\times SO(n)$
invariant. The method is inspired by constructions of Hsiang and these surfaces
generalize self-shrinking "tori" diffeomorphic to $S^{n-1}\times S^1$
constructed by Angenent.
