  Let $\lambda^{*}>0$ denote the largest possible value of $\lambda$ such that
$$ \{{array}{lllllll} \Delta^{2}u=\lambda(1+u)^{p} & {in}\ \ \B, %0<u\leq 1 &
{in}\ \ \B, u=\frac{\partial u}{\partial n} =0 & {on}\ \ \partial \B {array}.
$$ has a solution, where $\B$ is the unit ball in $R^{n}$ centered at the
origin, $p>\frac{n+4}{n-4}$ and $n$ is the exterior unit normal vector. We show
that for $\lambda=\lambda^{*}$ this problem possesses a unique weak solution
$u^{*}$, called the extremal solution. We prove that $u^{*}$ is singular when
$n\geq 13$ for $p$ large enough, in which case $u^{*}(x)\leq
r^{-\frac{4}{p-1}}-1$ on the unit ball.
