A process for manufacturing a piece made of composite material including a fiber preform that is embedded in a matrix, includes placing the preform in a first chamber that is delimited by a first semi-sealed wall, i.e., permeable to gas and impermeable to a product that is able to form the matrix, extracting the gases in a second chamber that is delimited by a second gas-tight wall and the first semi-sealed wall so as to obtain the diffusion of the product that is able to form the matrix in the preform, characterized in that it consists in using—as a first semi-sealed wall—at least one plate with a number of pipes of tapered shape that empty on either side of the at least one plate and at least one semi-sealed membrane that is superposed on the at least one plate.