This paper proposes a novel adaptive algorithm for nonlinear prediction of speech signals, which turns out to be the adaptation procedure for an order statistic LMS predictor. The LMS-L filter Pitas et al. addressed is modified to preserve the time information in the input vector for the adaptation, in which a coeficient matrix is utilized to update the predictor coeficients. Computer simulations demonstrate that the novel nonlinear predictor provides better performance than the Volterra quadratic predictor as well as the linear predictor.