The invention relates to a method of preparing crosslinked bitumen/polymer compositions having reduced emissions of hydrogen sulphide, in which, while operating at temperatures between 100° C. and 230° C. and with stirring, for a duration of at least ten minutes, at least one bitumen or mixture of bitumens is brought into contact with at least one polymer and at least one crosslinking agent, said crosslinking agent being represented by the general formula HS—R—SH where R represents a saturated or unsaturated, linear or branched, cyclic and/or aromatic hydrocarbon-based group having 2 to 40 carbon atoms, optionally comprising one or more heteroatoms, and that does not comprise a C═O carbonyl function and/or a O—C═O carboxylate function.