  We consider the nonlinear biharmonic Schr\"odinger equation
$$i\partial_tu+(\Delta^2+\mu\Delta)u+f(u)=0,\qquad (\text{BNLS})$$
  in the critical Sobolev space $H^s(\R^N)$, where $N\ge1$, $\mu=0$ or $-1$,
$0<s<\min\{\fc N2,8\}$ and $f(u)$ is a nonlinear function that behaves like
$\lambda\left|u\right|^{\alpha}u$ with
$\lambda\in\mathbb{C},\alpha=\frac{8}{N-2s}$. We prove the existence and
uniqueness of the global solutions to (BNLS) for the small initial data.
