Our aim in this communication is to improve the existing results concerning the stability of x(t) = Ax(t) + Bx(t - tau). It is shown that the unstable characteristic roots could be more accurately located in a bounded and restrictive region of the complex plane. An iterative scheme is presented for numerical implementation of the results. Numerical computations are presented for illustration and comparison with previous results. Copyright (C) 1996 Elsevier Science Ltd.