New algorithms for the computation of orthogonal and biorthogonal modulated lapped transforms(MLTs) are presented. The new structures are obtained by combining the MLT window operators with stages from a previously introduced structure for the type-IV discrete cosine transform (DCT-IV). The net result is fewer multiplications and additions than previously reported algorithms. For the orthogonal MLT, in particular, the new structure requires the computation of a slightly modified DCT-IV and some extra additions, but no further multiplications; so it demonstrates that the multiplicative complexity of the orthogonal MLT is the same as that of the DCT-IV.