A fiber preform is obtained by conforming panels of fiber texture on a former having a surface that reproduces the shape desired for a surface of the nozzle or the nozzle divergent section that is to be made. The panels are bonded together via their mutually contacting edges. A consolidated fiber reinforcement is formed by shaping the fiber preform impregnated with a consolidation composition including a resin. The shaping of the fiber preform is performed between the former and a jacket applied against the impregnated fiber preform so as the consolidated fiber reinforcement has a fiber volume percentage of at least 35%, and a thickness of less than 5 mm over at least a major fraction of its axial dimension. The densification of the fiber reinforcement is continued by chemical vapor infiltration after pyrolyzing the resin so that once densified, a part is obtained that has practically the shape and the wall thickness of the nozzle or the nozzle divergent section that is to be made.