In this paper we propose an alternative technique for producing digital Fresnel holograms. The evaluation of a diffraction pattern in a wide region is implemented in such a way as to avoid redundant calculations and preserve the precision. Because of the symmetry of the kernel, the complex amplitude is calculated at four points in the registration plane simultaneously. This algorithm decreases the required CPU time 4 times with respect to direct calculation. The digital Fresnel hologram is numerically and optically reconstructed, and some qualitative comparisons are made.