The present invention relates to the use of a stabilising composition free of derivatives of 6-aminouracyl or 6-aminothiouracyl type, and comprising at least one -diketone bearing two aromatic nuclei, at least one of which bears at least one substituent on one of the two orthopositions or on the paraposition; the said substituent being chosen from —R, —OR, —SR, —COOH, —O—CF₃ and —S—CF₃ radicals, in which formulae R is an alkyl radical. The invention also relates to halogenated polymers comprising such a stabilising composition.