A method of fabricating a part out of composite material, the method comprising the following steps: • forming a fiber texture from refractory fibers; • impregnating the fiber texture for a first time with a first slip containing first refractory particles; • eliminating the liquid phase from the first slip that has impregnated the fiber texture so as to leave within said texture only the first refractory particles; • impregnating the fiber texture for a second time with a second slip containing second refractory particles; • eliminating the liquid phase from the second slip that has impregnated the fiber texture so as to leave within said texture only the second refractory particles and obtain a fiber preform filled with the first and second refractory particles (151, 161); and • sintering the first and second refractory particles (151, 161) present in the fiber preform in order to form a refractory matrix in said preform; the method being characterized in that each of the first and second steps of impregnating the fiber texture comprises: • placing the fiber texture in a mold having an impregnation chamber including in its bottom portion a part made of porous material on which a first face of said texture rests, the impregnation chamber being closed in its top portion by a deformable impermeable diaphragm placed facing a second face of the fiber texture, said diaphragm separating the impregnation chamber from a compacting chamber; • injecting a slip (150; 160) containing a powder of refractory particles (151; 161) into the impregnation chamber between the second face of the fiber texture and the diaphragm; • injecting a compression fluid into the compacting chamber, the fluid exerting pressure on the diaphragm to force the slip to pass through the fiber texture; and in that each step of eliminating the liquid phase (152; 162) from the slip (150; 160) comprises draining the liquid phase of the slip that has passed through the fiber texture via the porous material part, the refractory particles (151; 161) being retained inside said texture by said porous material part. • forming a fiber texture from refractory fibers; • impregnating the fiber texture for a first time with a first slip containing first refractory particles; • eliminating the liquid phase from the first slip that has impregnated the fiber texture so as to leave within said texture only the first refractory particles; • impregnating the fiber texture for a second time with a second slip containing second refractory particles; • eliminating the liquid phase from the second slip that has impregnated the fiber texture so as to leave within said texture only the second refractory particles and obtain a fiber preform filled with the first and second refractory particles (151, 161); and • sintering the first and second refractory particles (151, 161) present in the fiber preform in order to form a refractory matrix in said preform; • placing the fiber texture in a mold having an impregnation chamber including in its bottom portion a part made of porous material on which a first face of said texture rests, the impregnation chamber being closed in its top portion by a deformable impermeable diaphragm placed facing a second face of the fiber texture, said diaphragm separating the impregnation chamber from a compacting chamber; • injecting a slip (150; 160) containing a powder of refractory particles (151; 161) into the impregnation chamber between the second face of the fiber texture and the diaphragm; • injecting a compression fluid into the compacting chamber, the fluid exerting pressure on the diaphragm to force the slip to pass through the fiber texture; and