Process for producing a ceramic matrix composite part by infiltration of a suspension of a ceramic powder into a fibre reinforcement which has not been preimpregnated, characterized in that it comprises the following steps: a) preparing a suspension of ceramic powder containing particles of chosen particle sizes dispersed in at least one solvent, in which the ceramic powder contains particles having a diameter which is from 5 to 10 times smaller than the size of the voids delimited by the fibres of which the fibre reinforcement (14; 114) is composed, and in which the suspension has a loading rate of particles sufficient that only a single infiltration step is required; b) positioning a fibre reinforcement (14; 114) in the form of plies of a fibre fabric, in a mould (12; 112); c) positioning on the fibre reinforcement (14; 114) a permeable membrane (16; 116) of chosen permeability, that is to say that is permeable to gases and/or to liquids, thus allowing a first cavity containing the fibre reinforcement to be closed; d) positioning an impermeable membrane (24; 124), which forms a counter-mould, thus allowing a second, tight cavity which is next to the first cavity and contains the first cavity to be closed; e) establishing a vacuum between the impermeable membrane and the permeable membrane, in the second cavity, so as to create the vacuum in the first cavity; f) injecting, into said first cavity, beneath the permeable membrane (16; 116), the suspension of ceramic powder of step a) into the fibre reinforcement, by means of a difference of pressure, the injection being carried out in a single infiltration step; g) removing the solvent through the permeable membrane in order to obtain an infiltrated preform; h) removing the infiltrated preform obtained in step g) from the mould; and i) sintering the infiltrated preform obtained in step h). a) preparing a suspension of ceramic powder containing particles of chosen particle sizes dispersed in at least one solvent, in which the ceramic powder contains particles having a diameter which is from 5 to 10 times smaller than the size of the voids delimited by the fibres of which the fibre reinforcement (14; 114) is composed, and in which the suspension has a loading rate of particles sufficient that only a single infiltration step is required; b) positioning a fibre reinforcement (14; 114) in the form of plies of a fibre fabric, in a mould (12; 112); c) positioning on the fibre reinforcement (14; 114) a permeable membrane (16; 116) of chosen permeability, that is to say that is permeable to gases and/or to liquids, thus allowing a first cavity containing the fibre reinforcement to be closed; d) positioning an impermeable membrane (24; 124), which forms a counter-mould, thus allowing a second, tight cavity which is next to the first cavity and contains the first cavity to be closed; e) establishing a vacuum between the impermeable membrane and the permeable membrane, in the second cavity, so as to create the vacuum in the first cavity; f) injecting, into said first cavity, beneath the permeable membrane (16; 116), the suspension of ceramic powder of step a) into the fibre reinforcement, by means of a difference of pressure, the injection being carried out in a single infiltration step; g) removing the solvent through the permeable membrane in order to obtain an infiltrated preform; h) removing the infiltrated preform obtained in step g) from the mould; and i) sintering the infiltrated preform obtained in step h).