Process for the elimination of mercury contained in a heavy hydrocarbon-containing feedstock downstream of a main fractionation unit, a process in which: a) the non-elemental mercury contained in the compounds of said feedstock is transformed to elemental mercury; b) a fractionation of said hydrocarbon-containing feedstock is carried out in a fractionation unit in order to produce a top effluent comprising elemental mercury; c) the top effluent obtained in stage b) is brought into contact with a mercury capture material contained in a unit for the capture of mercury, in order to obtain an effluent that is at least partially de-mercurized.