  We show that every gravitational instantons are SU(2) Yang-Mills instantons
on a Ricci-flat four manifold although the reverse is not necessarily true. It
is shown that gravitational instantons satisfy exactly the same self-duality
equation of SU(2) Yang-Mills instantons on the Ricci-flat manifold determined
by the gravitational instantons themselves. We explicitly check the
correspondence with several examples and discuss their topological properties.
