We consider hyper-Kaehler manifolds of complex dimension 4 which are fibrations. It is known that the fibers are abelian varieties and the base is $\mathbb P^2$. We assume that the general fiber is isomorphic to a product of two elliptic curves. Our result is that such a hyper-Kaehler manifold is deformation equivalent to a Hilbert scheme of two points on a K3 surface.