The invention concerns an improved method of combustion of a solid hydrocarbonaceous feedstock in a chemical loop, implementing a particular configuration of the reduction area with: a first reaction area (R1) operating as a dense fluidised bed; a second reaction area (R2); a rapid separation area (S3) for separating unburned solid feedstock particles, fly ash and particles of oxygen carrier materials in a mixture coming from the area (R2); a dedusting of the smoke (S4); an area (D7) for dividing the stream of particles, one portion of the particles being directly recycled towards the first reaction area (R1), the other being sent to an elutriation separation area (S5) to recover the ash via a pipe (18) and recycle the dense particles via a pipe (20) to the first reaction area (R1). The invention also concerns a chemical looping combustion facility used to implement said method.