The automatic braking process is triggered when a threshold level for the rate of actuation of the braking pedal is exceeded. During the braking process a brake pressure higher than that corresp. to the position of the brake pedal is generated and the braking process is terminated when a termination criterion is fulfilled. During a time interval after fulfilment of the termination criterion the triggering threshold level is reduced by a factor. The reduction of the triggering threshold level may only be performed if the termination criterion is fulfilled within a defined period after the triggering criterion is fulfilled.