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The impulse-noise cancelling device recently described by W.L. Black [IEEE Trans on Comm. Systems, vol. CS-11, p. 506; December, 1963] has in principle two noteworthy properties that he did not mention. First, the canceller does not fail completely when two noise pulses overlap in time, since the residual d.isturbance, if the two pulse responses are very different in magnitude, is ideally of the order of magnitude of the smaller pulse response. Second, complete cancellation requires that the two auxiliary channels be clear channels free of interference. If interference is present, there i13 a residuum, after cancellation, of the order of magnitude of the interference, and if the interference is of the order of magnitude of the desired signal in the signal channel, the canceller at best is not very much better than a simple (reliable) noise limiter. Proof of these properties follows.