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The linear prediction (LP) algorithm can be regarded as one that leads to the estimation of a set of zero-forcing equalizers. A final step in the LP algorithm consists in (linearly) combining these equalizers to form one that restores the transmitted symbols ISI-free, unattenuated and not delayed. We show that the way they were originally combined is not justified. We propose and justify a different combination of the original LP equalizers. The modified LP algorithm shows enhanced performances for both equalization and identification tests. We also comment on the often questioned robustness of the LP algorithm to channel order over estimation. We argue here that the LP algorithm is truly robust to order over estimation and we give a formal proof to this.