A method for recovering fibers embedded in a composite material, comprising the steps of: - loading a first furnace chamber with a volume of the composite material; - thermolyzing the composite material in the first furnace chamber, resulting in a gaseous fraction that is continuously evacuated from the furnace chamber, and a residue of fibers covered with char that is left in the furnace chamber; - cracking the gaseous fraction from the thermolysis step, resulting in a mixture of condensable and non-condensable gases; - loading a second furnace chamber with a volume of the composite material; - injecting a stream of an oxygen-containing gas into the still hot first furnace chamber after the thermolysis is completed therein, in order to burn the char from the fibers in an exothermic combustion; - thermolyzing the composite material in the second furnace chamber, with heat being contributed by the combustion that is taking or has taken place in the first furnace chamber, resulting in a gaseous fraction that is continuously evacuated from the second furnace chamber, and a residue of fibers covered with char that is left in the second furnace chamber; - cracking the gaseous fraction from the thermolysis step in the second furnace chamber, resulting in a mixture of condensable and non-condensable gases; - unloading the clean fibers from the first furnace chamber and loading the latter with a volume of the composite material; - injecting a stream of an oxygen-containing gas into the still hot second furnace chamber after the thermolysis is completed therein, in order to burn the char from the fibers in an exothermic combustion; - thermolyzing the composite material in the first furnace chamber, with heat being contributed by the combustion that is taking or has taken place in the second furnace chamber, resulting in a gaseous fraction that is continuously evacuated from the first furnace chamber, and a residue of fibers covered with char that is left in the first furnace chamber; - cracking the gaseous fraction from the thermolysis step in the first furnace chamber, resulting in a mixture of condensable and non-condensable gases; - unloading the clean fibers from the second furnace chamber and loading the latter with a volume of the composite material; - injecting a stream of an oxygen-containing gas into the still hot first furnace chamber after the thermolysis is completed therein, in order to burn the char from the fibers in an exothermic combustion. - loading a first furnace chamber with a volume of the composite material; - thermolyzing the composite material in the first furnace chamber, resulting in a gaseous fraction that is continuously evacuated from the furnace chamber, and a residue of fibers covered with char that is left in the furnace chamber; - cracking the gaseous fraction from the thermolysis step, resulting in a mixture of condensable and non-condensable gases; - loading a second furnace chamber with a volume of the composite material; - injecting a stream of an oxygen-containing gas into the still hot first furnace chamber after the thermolysis is completed therein, in order to burn the char from the fibers in an exothermic combustion; - thermolyzing the composite material in the second furnace chamber, with heat being contributed by the combustion that is taking or has taken place in the first furnace chamber, resulting in a gaseous fraction that is continuously evacuated from the second furnace chamber, and a residue of fibers covered with char that is left in the second furnace chamber; - cracking the gaseous fraction from the thermolysis step in the second furnace chamber, resulting in a mixture of condensable and non-condensable gases; - unloading the clean fibers from the first furnace chamber and loading the latter with a volume of the composite material; - injecting a stream of an oxygen-containing gas into the still hot second furnace chamber after the thermolysis is completed therein, in order to burn the char from the fibers in an exothermic combustion; - thermolyzing the composite material in the first furnace chamber, with heat being contributed by the combustion that is taking or has taken place in the second furnace chamber, resulting in a gaseous fraction that is continuously evacuated from the first furnace chamber, and a residue of fibers covered with char that is left in the first furnace chamber; - cracking the gaseous fraction from the thermolysis step in the first furnace chamber, resulting in a mixture of condensable and non-condensable gases; - unloading the clean fibers from the second furnace chamber and loading the latter with a volume of the composite material; - injecting a stream of an oxygen-containing gas into the still hot first furnace chamber after the thermolysis is completed therein, in order to burn the char from the fibers in an exothermic combustion.