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A new recursive fast radix-2 algorithm for an efficient computation of the modulated complex lapped transform (MCLT) is presented. Based on a new proposed alternative recursive sparse matrix factorization for the MDCT (modified discrete cosine transform) matrix and a relation between the MDCT and the MDST (modified discrete sine transform), firstly a new recursive fast radix-2 MDST algorithm is derived. The corresponding fast MDCT and MDST computational structures are regular and complementary to each other. Consequently, this fact enables us by their composition to construct a fast MCLT computational structure representing the fast recursive radix-2 MCLT algorithm. The fast MCLT computational structure is regular and all its stages may be realized in parallel. Combining the proposed fast radix-2 MCLT algorithm with an existing generalized fast mixed-radix MDCT algorithm defined for the composite lengths N = 2 × qm, m ≥ 2, where q is an odd positive integer, we can compute the MCLT for the composite lengths N = 2n × qm, n, m ≥ 2, thus supporting a wider range of transform sizes compared to existing fast MCLT algorithms.