  We consider the fourth order Schr\"odinger operator $H=\Delta^2+V(x)$ in
three dimensions with real-valued potential $V$. Let $H_0=\Delta^2$, if $V$
decays sufficiently and there are no eigenvalues or resonances in the
absolutely continuous spectrum of $H$ then the wave operators $W_{\pm}=
s\,-\,\lim_{t\to \pm \infty} e^{itH}e^{-itH_0}$ extend to bounded operators on
$L^p(\mathbb R^3)$ for all $1<p<\infty$.
