The study of Fraunhofer diffraction of a Gaussian laser beam by a computer-generated, binary four-sector grating (FSG) is presented. In the four equal angular sectors of the FSG, parts of a binary rectilinear grating are embedded in such a way that, two neighboring parts are shifted by a half spatial rectilinear grating period. Analytical expressions, describing the diffracted wave field amplitude and intensity distributions in the focal plane of a converging lens, are derived. The zeroth-diffraction-order beam is a Gaussian beam whose transverse cross section has a reduced Gaussian radius. The higher-diffraction-order beam transverse intensity profiles have four bright spots divided by dark crossed lines and a central dark, non-vortex core. They can be described as cosine-Laguerre-Gaussian Kummer beams. The numerically calculated diffraction patterns, as well as the interference patterns of the diffracted beam with a slightly inclined plane wave, are supported by experimentally obtained ones. In both investigations (theoretical and experimental) the interferograms confirm the non-vortex nature of the diffraction spots.