A process for producing a cross-linked bitumen/polymer composition (PmB) with a reduction in hydrogen sulphide (H2S) emissions including a production unit for the implementation of such a process. The production process includes the following successive steps:(a) preparing a cross-linked bitumen/polymer composition (PmB) in a reactor and,(b) transferring a predetermined quantity of the composition from the reactor to a storage tank and/or directly to a loading station via a distribution line, the composition being maintained at a temperature between 100° C. and 220° C. during the transfer. A reduction in hydrogen sulphide emissions (H2S) is carried out by the in-line injection of an effective quantity of a hydrogen sulphide (H2S) scavenger during the transfer step. The injection is carried out by continuous introduction of the hydrogen sulphide (H2S) scavenger into the distribution line downstream of the reactor and, upstream of the storage tank and the loading station.