The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and Sandler [10] and utilizes the vectorization of calculating process at each stage of the considered transformation. This allows for the use of a computational process parallelization and results in a reduction of computation time. In the description of the computational procedure, which describes the algorithm, we use the matrix notation. This notation enables to represent adequately the space-time structures of the implemented computational process and directly map these structures into the constructions of a high-level programming language or into a hardware realization space.