This paper proposes ADAPTIVE STOCHASTIC ITERATION ALGORITHM that can be used for the full-duplex digital data transmission over existing twisted-pair cables. The canceller step size changes according to the residual echo level. Thus convergence speed increases by an order of magnitude over the conventional stochastic interation alogorithm. And it can be combined with the sequential type adaptive digital filter that simplifies the conventional echo canceller circuit. Thus it is suitable for LSI implementation. Theoretical analysis on two algorithms is carried out and the algorithm simulation program is developed.