Abstract: I shall be talking about the De Rham decomposition theorem. I will show that if the holonomy group of a simply connected complete Riemannian manifold M splits into a direct sum as a linear group acting on the tangent space (reducibility) then the manifold M is isometric to the direct product of an Euclidean space with k simply connected, complete, irreducible Riemannian manifolds. Such a decomposition is unique up to order k.