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In this paper we present a new two-step maximum likelihood (TSML) algorithm for estimating the impulse responses of multiple FIR channels driven by an arbitrary unknown input. In Hua (1996), the original TSML method was developed as a fast alternative to the direct maximum likelihood approach. The TSML method exploits a novel orthogonal complement (OC) matrix of the block Sylvester matrix. Despite its high-SNR (signal-to-noise-ratio) efficiency, the TSML method is still computationally expensive as it requires approximately O(q/sup 3/N/sup 3/) flops, where N is the sample size and q is the number of system outputs. The contribution in this paper consists in introducing a new TSML method which exploits a non-redundant OC matrix whose column vectors are shown to form a basis of the noise subspace. The new TSML method is shown to require only O(q/sup 3/N/sup 2/) flops. Like the original TSML method, the new TSML method requires no initial estimates and is asymptotically (high SNR) optimum.