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A fast (computationally efficient) least squares algorithm to fit a Mth order linear phase (symmetric) FIR system to an input/output sequence was presented in reference . This algorithm solved the normal equations associated with the least squares procedure with a number of computations proportional to M2, rather than M3as required for general purpose linear equation algorithms. The linear phase system identification problem occurs in certain signal processing applications where no phase distortion is a requirement. The fast algorithm is possible due to the near-to-Toeplitz plus-Hankel-property of the normal equation matrix. The algorithm reported in  required 2NM + 24M2operations, where N is the number of data samples. This paper describes some additional properties that further reduces this complexity to 2NM + 18M2. This results in a computational savings of 15% to 20% for typical values of N and M.