In this paper a new adaptive scheme is proposed to identify SISO linear systems. The algorithm has its origin in the stochastic approximation method well-known in statistics and it differs from a widely studied adaptive identifier only by a time-varying gain term. We show that this simple modification makes the algorithm robust to the presence of noise in the estimation process, using methods that emphasize the connection with the standard stability analysis used in the deterministic theory of adaptive systems. The robustness properties are then demonstrated in a number of simulation studies.