The recognition of the digital curve arches in the structural analysis of images is one of the tasks of the visual information processing in the systems of artificial intellect. The use of curve arches as the structural elements of images will approach their description to intuitive, human interpretation, essentially reduce memory expenses for a visual information storage and processing time. In the article the definition of a digital curve arch is considered, from which the algorithm is developed to define if a part of a contour is really a smooth curve arch or not.