Abstract: The object of study is shaping of the curve of the line on a discrete set of source data. In this case, a discrete series of points-nodes with tangents in them and the value of the curvature of the first segment in its initial node are taken as initial data. The subject of the study is a fractional rational Bezier curve of the second order. The authors investigate in detail the aspects of obtaining segments of rational Bezier curves in the direction of docking their C2 smoothness in order to obtain a Bezier spline.A mathematical method is applied based on the analytical representation of fractional rational Bezier segments of the second order using the apparatus of mathematical analysis and differential calculus. The novelty of the study lies in the fact that the obtained mathematical model of the spline allows you to directly indicate in the process of shaping the types of segments that make it up: parabolic, elliptical or hyperbolic. It is shown that the standard form of the Bezier curve representation can be reduced to a simpler form. This proposed model is qualitatively different from existing models. Numerical examples of obtaining open and closed Bezier spline are considered.