In this paper we propose a series-parallel adaptive algorithm using the square sum of the correlation function and its convergence condition. It is known well that this adaptive algorithm is robust for the near-end noise since that does not have the bias error of the adaptive weights but the loop gain ensuring the convergence is not clear. We show that the independent adaptive control of two adaptive filters is possible and formulate the convergence condition of the loop gain. The analytical results and the above mentioned feature are verified by computer simulation.