  In this paper, we show that the center of every Coxeter group is finite and
isomorphic to $(\Z_2)^n$ for some $n\ge 0$. Moreover, for a Coxeter system
$(W,S)$, we prove that $Z(W)=Z(W_{S\setminus\tilde{S}})$ and
$Z(W_{\tilde{S}})=1$, where $Z(W)$ is the center of the Coxeter group $W$ and
$\tilde{S}$ is the subset of $S$ such that the parabolic subgroup
$W_{\tilde{S}}$ is the {\it essential parabolic subgroup} of $(W,S)$ (i.e.\
$W_{\tilde{S}}$ is the minimum parabolic subgroup of finite index in $(W,S)$).
The finiteness of the center of a Coxeter group implies that a splitting
theorem holds for Coxeter groups.
