In a network with switching elements, a transmission path is found in that each destination address at a switching element is allocated a group of outputs via which messages can be transmitted to this destination address. Within this group of outputs, a search is made for a free output and messages are buffered as long as there is no output free within this group. Thus, in the process, there is deliberately no exclusive use of a specific output and each destination address is allocated a plurality of possible outputs. As a result, the probability of a blockage of outputs is reduced and the network throughput is increased.