A method for chemical-looping combustion of a hydrocarbon feedstock of solid particles, wherein an oxygen-carrying material circulates in form of particles, comprising: - contacting hydrocarbon feedstock particles with the oxygen-carrying material particles in a reduction zone R0, - contacting oxygen-carrying material particles from reduction zone R0 with an oxidizing gas stream in a reactive oxidation zone R1, - separating the fly ashes, the fines and the oxygen-carrying material particles within a mixture from zone R1 by dilute phase elutriation in a dilute phase separation zone S2 so as to discharge through a discharge line a gaseous effluent comprising the major part of the fly ashes and of the oxygen-carrying material fines, and to send a particle stream comprising the major part of the oxygen-carrying particles to reduction zone R0, the driving force required for dilute phase elutriation in S2 being provided by the oxidizing gas stream coming from reactive oxidation zone R1, - carrying out deep separation of the ashes, the fines and the oxygen-carrying particles in a dedusting zone S4 in order to discharge a gas stream containing the major part of the ashes and the fines, and a particle stream containing the major part of the oxygen-carrying material that is sent through a delivery line to reduction zone R0, and characterized in that: - carrying out dense phase elutriation separation in a dense phase elutriation separation zone S5 arranged downstream from dedusting zone S4 and fluidized by a non-reducing gas allowing to separate the fly ashes from the oxygen-carrying material in particle stream in order to send a particle stream rich in oxygen-carrying particles to reduction zone R0 and to discharge a gas stream rich in fly ashes. - contacting hydrocarbon feedstock particles with the oxygen-carrying material particles in a reduction zone R0, - contacting oxygen-carrying material particles from reduction zone R0 with an oxidizing gas stream in a reactive oxidation zone R1, - separating the fly ashes, the fines and the oxygen-carrying material particles within a mixture from zone R1 by dilute phase elutriation in a dilute phase separation zone S2 so as to discharge through a discharge line a gaseous effluent comprising the major part of the fly ashes and of the oxygen-carrying material fines, and to send a particle stream comprising the major part of the oxygen-carrying particles to reduction zone R0, the driving force required for dilute phase elutriation in S2 being provided by the oxidizing gas stream coming from reactive oxidation zone R1, - carrying out deep separation of the ashes, the fines and the oxygen-carrying particles in a dedusting zone S4 in order to discharge a gas stream containing the major part of the ashes and the fines, and a particle stream containing the major part of the oxygen-carrying material that is sent through a delivery line to reduction zone R0, and characterized in that: - carrying out dense phase elutriation separation in a dense phase elutriation separation zone S5 arranged downstream from dedusting zone S4 and fluidized by a non-reducing gas allowing to separate the fly ashes from the oxygen-carrying material in particle stream in order to send a particle stream rich in oxygen-carrying particles to reduction zone R0 and to discharge a gas stream rich in fly ashes.