A Levinson-type recursion for a class of non-Teoplitz systems of linear equations is demonstrated. A complete solution is expressed as a linear combination of a partial solution and three auxiliary solutions. The class of systems possesses a special structure in that the coefficient matrices can be partitioned into four block Teoplitz submatrices. The number of multiplications and additions required to compute an n- dimensional solution if O(n2). The recursion is then applied to multichannel IIR filtering. Specifically, a lattice structure is established for linear minimum mean square error predictors having independently and arbitrarily specified numbers of poles and zeros. Next the recursion is used to develop a fast time and order recursive algorithm for ARX system identification, producing parameter estimates of family of ARX models. The algorithm preserves consistency of the well-known recursive least-squares algorithm.