An alternate algorithm to compute the discrete cosine transform (DCT) of sequences of arbitrary number of points is proposed. The algorithm consists of partitioning the DCT kernel into submatrices which by proper row and column shuffling and negations can be made equivalent to the group tables (or parts of them) of appropriate Abelian groups. The computations pertaining to the submatrices can be carried out using multidimensional cyclic convolutions. Algorithms are also developed to perform the computations associated with the submatrices that are parts of larger group tables. The new algorithms are more versatile and generally better in terms of the computational complexity in comparison with the existing algorithms.