This brief proposes an approach to apply least-squares techniques to adaptive FIR filtering in cascade form. A triangular structure is combined with an adaptive multichannel filter, which can exploit a fast recursive least squares (RLS) algorithm. The resulting approximation and the behavior of the system in the learning case is discussed. Simulations results are given for the linear prediction case, for which an additional adaptive procedure is derived. Sinusoidal signals are used at the input. since the inherent cascade structure directly yields the frequencies of the sinusoids from the section coefficients. The proposed method brings the efficiency of least-squares techniques, in terms of accuracy and convergence rate, to adaptive filter in cascade form.449757762