  In this article we show the existence of closed embedded self-shrinkers in
$\Bbb{R}^{n+1}$ that are topologically of type $S^1\times M$, where $M\subset
S^n$ is any isoparametric hypersurface in $S^n$ for which the multiplicities of
the principle curvatures agree. This yields new examples of closed
self-shrinkers, for example self-shrinkers of topological type $S^1\times
S^k\times S^k\subset \Bbb R^{2k+2}$ for any $k$. If the number of distinct
principle curvatures of $M$ is one the resulting self-shrinker is topologically
$S^1\times S^{n-1}$ and the construction recovers Angenent's shrinking
doughnut.
