The Bezier curves appears the fundamental basis of many applications for computer graphics. Intuitively clear geometrical interpretation of the Bezier curves allows to assume that they can be effectively used in the tasks of pattern recognition. One of such tasks can be binary raster images perception. In this case the use of the Bezier curves guarantees the invariance of algorithms of recognition to affine transformations. However much the wide use of the Bezier curves in the tasks of pattern recognition restrains by complication of computational algorithms of approximation of experimental data by parametric splines which the Bezier curves are. The iteration algorithm of middle calculable complication, which enables to approximate the areas of contour of binary image or other experimental data described to the smooth curve with one or two extremums, is expounded in the represented publication.