The Seiberg-Witten map which appears in the context of non-Abelian gauge theories on noncommutative spaces is studied from the point of view of its cohomology. The equations defining the map are expressed through a coboundary operator. This allows us to find solutions by constructing a suitable homotopy operator. The method can be applied to any order in theta and for any gauge group. It clarifies the nature of the ambiguities which arise in the map.