This paper proposes an adaptive algorithm for identifying unknown systems containing nonlinear amplitude characteristics. Usually, the nonlinearity is so small as to be negligible. However, in low cost systems, such as acoustic echo canceller using a small loudspeaker, the nonlinearity deteriorates the performance of the identification. Several methods preventing the deterioration, polynomial or Volterra series approximations, have been hence proposed and studied. However, the conventional methods require high processing cost. In this paper, we propose a method approximating the nonlinear characteristics with a piecewise linear curve and show using computer simulations that the performance can be extremely improved. The proposed method can also reduce the processing cost to only about twice that of the linear adaptive filter system.