We prove that the versal deformation space R of a (not necessarily indecomposable) maximal Cohen-Macaulay module M on a simple singularity X of even dimension is irreducible (in contrast to the odd dimensional case). Assuming dim X even, we show that Sing Rred has one or two components, and we give the codimension. We give further properties of the local deformation relation, in particular we completely describe how any indecomposable M (locally) deforms. In dimension two the proofs proceed by investigating a partial order defined by the intersection form, applying the McKay correspondence and an existence result of A. Ishii. The general case follows by applying the functor introduced by H. Knörrer.