A method implemented in a vehicle, using information representative of an operational state of the vehicle being provided by sensors and a data communication bus. The information is representative of the engagement and disengagement of an exploitation assistance brake (EAB) and a speed of the vehicle and of a pressure on a brake pedal of the vehicle. A cut-off condition (C3) for the thermal engine can be validated when the speed is lower than a predetermined threshold and in the case where pressure is applied on the brake pedal or when the exploitation assistance brake is activated. The system includes at least one sensor for the condition of the exploitation assistance brake.