The connection between renormalization schemes (RS's) and the renormalization group (RG) functions for a massive Yang-Mills theory is investigated. The RS's are defined in a manner independent of the regularization procedure. The RS transformations are defined in such a way that it is clear that they form a group. It is shown that to a given set of RG functions corresponds an infinite number of RS's. The subgroup of RS transformations which leave invariant the (mass-shell) MS-RG functions is carefully described. Gauge invariance, regularity of the theory when m —> 0 and mass decoupling are imposed and the corresponding indeterminations of RS's are given. It is seen that a RS which fulfills simultaneously the above conditions does not exist.