  In this paper, we study complete self-shrinkers in Euclidean space and prove
that an $n$-dimensional complete self-shrinker in Euclidean space
$\mathbb{R}^{n+1}$ is isometric to either $\mathbb{R}^{n}$, $S^{n}(\sqrt{n})$,
or $S^k (\sqrt{k})\times\mathbb{R}^{n-k}$, $1\leq k\leq n-1$, if the squared
norm $S$ of the second fundamental form, $f_3$ are constant and $S$ satisfies
$S<1.83379$. We should remark that the condition of polynomial volume growth is
not assumed.
