The present invention relates to a sheath (7) for a cable (1), where the sheath contains, at least in part, a halogen-free intumescent composition. The composition of the sheath contains a mixture of a polymer matrix chosen from a polyethylene, a polypropylene, an ethylene copolymer, a propylene copolymer, a silicone, a polyamide, and a mixture thereof and at least one flame-retardant additive. The flame retardant additive has a first inorganic compound having a lamellar crystal structure, and a second inorganic compound inserted between the lamellae of the first compound, where the second compound causes the lamellae to move apart under the application of heat.