We introduce and study the family of sets in a finite dimensional Enclidean space which can be written as the Minkowsky sum of an open, convex  and bounded set and a closed and convex set. We establish several properties of the class of such sets, called OM-decomposable, some of which extend related properties which hold for the class of Motzkin decomposable sets (i.e., those for which the convex and bounded set in the decomposition is required to be closed, hence compact).