The Ostrowski-Reich theorem (O-R theorem) states that for a system \(Ax=b\) of linear equations with A nonsingular, if A is Hermitian and if the diagonal of A is positive, then the SOR method converges for each relaxation parameter in (0,2) if and only if A is positive definite. In this paper, we define a generalized AOR method and generalize the O-R theorem to the AOR method. Our results imply the O-R theorem.