As you know, a radical means to prevent skidding of the vehicle (TK) during braking is the use of such integrated automatic active safety systems as anti-lock braking system (ABS), emergency brake booster, traction control system (TRC), electronic brake force distribution system EBD), stability control system (VSC), tire pressure monitoring system (TPWS), electronic control brake system (ECB), electric power steering (EPS), integrated dynamic vehicle control system (VDIM). Also, the stable position of the vehicle when driving on the road is provided by a set of automatic devices (for example dynamic stabilization system, anti-lock and anti-slip systems, etc.). Most of the cases of violation of the stable position of the vehicle on the road are related to the process of its braking. The article considers an alternative approach to stabilizing the position of the vehicle on the road during braking due to another approach to the management of its braking system. The mathematical description and schemes of position of the vehicle in the course of braking are offered. The stability of the position of the vehicle is ensured by braking the rear wheels, or braking one of the rear wheels (internal in relation to the direction of skidding), due to the system of dynamic stabilization of the course angle. Braking of the rear wheels during the initial skidding during braking allows you to stabilize the course angle of the vehicle (with full braking of the rear wheels, the stabilization time is minimal). This significantly reduces the braking efficiency of the vehicle, as only the front wheels are brake. Braking of only one rear wheel allows to provide identical duration of transition process at the highest efficiency of braking of the vehicle. On the example of a conventional vehicle, a comparative analysis of the effectiveness of the methods of dynamic stabilization of the course angle by braking one and two rear wheels.