  For a Coxeter group $W$ we have an associating bi-linear form $B$ on suitable
real vector space. We assume that $B$ has the signature $(n-1,1)$ and all the
bi-linear form associating rank $n' (\ge 3)$ Coxeter subgroups generated by
subsets of $S$ has the signature $(n',0)$ or $(n'-1,1)$. Under these
assumptions, we see that there exists the Cannon-Thurston map for $W$, that is,
the $W$-equivariant continuous surjection from the Gromov boundary of $W$ to
the limit set of $W$. To see this we construct an isometric action of $W$ on an
ellipsoid with the Hilbert metric. As a consequence, we see that the limit set
of $W$ coincides with the set of accumulation points of roots of $W$.
