h m i n g identification is one of the most widely utilized adaptive algorithms due to its small computational complexity. A problem with this algorithm is that a division by the square norm of the state vector is included in the coefficient update process which easily produces an instability when the nonstationary signal such as speech is given as the input. A method known to cope with such a problem and to realize the stable convergence involves not updating the coefficient when small input signals contin-. This paper discusses this approach. As a first step, the situation is assumed where the square norm of the state vector is less than the specified threshold and the effect of interrupting the coefficient update is analyzed. The convergence and the timeconstant are formulated and the guarantee of the estimation accuracy for the convergence value is discussed. Then, the step gain is derived for the specified guarantee value so that the convergence speed is the fastest in the stochastic sense while ensuring stability. Lastly, the effectiveness of the proposed method is verified by computer simulation. It is shown that, even if the input signal is nonstationary, the fastest convergence speed is realized, together with the satisfactory estimation accuracy, which is always obtained according to the specified guarantee value after the convergence.