Abstract Let Out ( RG ) be the set of all outer R -automorphisms of a group ring RG of arbitrary group G over a commutative ring R with 1. It is proved that there is a bijective correspondence between the set Out ( RG ) and a set consisting of R ( G × G )-isomorphism classes of R -free R ( G × G )-modules of a certain type. For the case when G is finite and R is the ring of algebraic integers of an algebraic number field the above result implies that there are only finitely many conjugacy classes of group bases in RG . A generalization of a result due to R . Sandling is also provided.