  In the paper, by constructing a initial data $u_{0}\in B^{\sigma}_{p,\infty}$
with $\sigma-2>\max\{1+\frac 1 p, \frac 3 2\}$, we prove that the corresponding
solution to the higher dimensional Camassa-Holm equations starting from $u_{0}$
is discontinuous at $t=0$ in the norm of $B^{\sigma}_{p,\infty}$, which implies
that the ill-posedness for the higher dimensional Camassa-Holm equations in
$B^{\sigma}_{p,\infty}$.
