A brake system for a vehicle has at least one pressure supply device which is connected to a brake circuit via a hydraulic line. Furthermore, the brake system has a hydraulic connection between at least one of the brake circuits and an accumulator container, said connection being switchable via at least one outlet switch valve, and the pressure supply device has a double stroke piston with a working stroke and a return stroke. The double stroke piston can be at least partly emptied via the outlet switch valve.