The diffraction of a scalar wave field incident on a flat irregular diffraction grating with arbitrarily oriented rectangular apertures is considered. It is shown that if the random grating is illuminated from the far zone (the diffraction problem in the Fraunhofer formulation), then the diffraction field in the far zone (the Fraunhofer picture) can have a regular structure. It has been proven that the Fraunhofer diffraction pattern in the Fraunhofer formulation does not depend on the relative position of the apertures, but is determined by their relative orientation. This study highlights the important role of laser beam size and shape in diffraction problems, which is often overlooked in research.A discussion of the statistical properties of the diffraction pattern is carried out on the basis of corresponding calculations of the scattered field intensity averaged over random parameters of the structure. The presented theoretical study explains the diffraction patterns in the form of concentrated circles observed on a system of rectangular NaCl microcrystals deposited randomly on a flat glass substrate. It is important that this work brings a certain understanding to the problematic of inverse diffraction problems, when symmetric diffraction patterns are associated with an ideally structured grating. At the same time, as this work shows, symmetric diffraction patterns can also be realized in the case of random gratings.