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For each $n\geq 2$ we construct a new closed embedded mean curvatureself-shrinking hypersurface in $\mathbb{R}^{2n}$. These self-shrinkers arediffeomorphic 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 surfacesgeneralize self-shrinking "tori" diffeomorphic to $S^{n-1}\times S^1$constructed by Angenent.

Closed Mean Curvature Self-Shrinking Surfaces of Generalized Rotational Type