A method of assembling together by brazing two parts made of composite material, each part having an assembly face for brazing with the assembly face of the other part, the method including: making a plurality of cavities in the assembly face of at least one of the two composite material parts, at least some of the cavities opening out into one or more portions of the part that are situated outside the assembly face; interposing capillary elements between the assembly faces of the composite material parts; placing a brazing composition in contact with a portion of the capillary elements; and applying heat treatment to liquefy the brazing composition so as to cause the molten brazing composition to spread by capillarity between the assembly faces of the composite material parts.