The transmission restoration for faulty operating paths is generally constituted by a direct transmission restoration or a centrally controlled transmission rerouting. In the substitute direct transmission rerouting, N restoration links are permanently assigned to M operating paths, so that when faults affect more than N operating paths, M-N operating paths do not have the possibility to switch to the restoration link. With the centrally controlled transmission rerouting the employment of the restoration link requires reporting this fault to the supervising station as well as transmitting the control message from the supervising station to the switching matrices. The time required thereto generally causes all connections through the faulty operating path to be broken. By means of decentralized controlled transmission rerouting in which the rerouting control devices positioned after the location of the fault in the direction of transmission take over the master function for the transmission direction involved, one restoration link is always determined, in a simple manner and independent of each other, which need not perforce be led along the same route or in the same transmission system. Hence, a restoration link in the relevant direction of transmission can be determined and switched to immediately without the monitoring devices which detect the fault in the message transmission system having to communicate with each other.