A brake system for a motor vehicle including front wheel brakes, rear wheel brakes, and a hydraulic system supplying hydraulic fluid to the wheel brakes. An electronic brake control connected to the hydraulic system actuates the hydraulic system to build up a brake pressure and supply the wheel brakes with the hydraulic fluid. The system includes a parking brake system that activates the rear wheel brakes. The electronic brake control actuates the hydraulic system to build up a brake pressure and at the beginning of an emergency braking procedure closes valves of the hydraulic system associated with the rear wheel brakes, opens valves of the hydraulic system associated with the front wheel brakes, and activates the parking brake system while keeping the valves of the hydraulic system associated with the rear wheel brakes closed for a period of adjustable length.