Let $G$ be a semisimple algebraic group defined over an algebraically closed field $K$ of good characteristic $p>0.$ Let $u$ be a unipotent element of $G$ of order $p^{t}$, for some $t\in {\Bbb N}$. In this paper it is shown that $u$ lies in a closed subgroup of $G$ isomorphic to the {\it Witt group} $W_{t}(K),$ which is a $t$-dimensional connected abelian unipotent algebraic group. 2000 Mathematics Subject Classification: 20G15.