  In this note, we investigate fibre space structures of a projective
irreducible symplectic manifold. We prove that an 2n-dimensional projective
irreducible symplectic manifold admits only an n-dimensional fibration over a
Fano variety which has only Q-factorial log-terminal singularities and whose
Picard number is one. Moreover we prove that a general fibre is an abelian
variety up to finite unramified cover, especially, a general fibre is an
abelian surface for 4-fold.
