A modification of a previously published two-dimensional phase-retrieval algorithm based on the sampling theorem [ Opt. Commun. 47, 380 (1983)] is introduced. With an appropriate choice of the intermediate sampling grid, a significant reduction in the number of computations is achieved, because an independent system of equations may be solved for each line of the Fourier transform of the object. The results of computer simulations on real objects are given. The algorithm converges rapidly.