  Let $X$ be an irreducible holomorphic symplectic fourfold and $D$ a smooth
hypersurface in $X$. It follows from a result by Amerik and Campana that the
characteristic foliation (that is the foliation given by the kernel of the
restriction of the symplectic form to $D$) is not algebraic unless $D$ is
uniruled. Suppose now that the Zariski closure of its general leaf is a
surface. We prove that $X$ has a lagrangian fibration and $D$ is the inverse
image of a curve on its base.
