A method of fabricating a sector (12; 1012) out of composite material for a turbine nozzle or a compressor diffuser of a turbine engine, the method comprising: • making single-airfoil unit vanes (112; 412; 612; 812 1, 812 2) for a turbine nozzle or a compressor diffuser, each having an inner platform (114; 414; 614; 814a, 815a), an outer platform (116; 416; 616; 816a, 817a), and an airfoil extending between the inner and outer platforms and secured thereto, each nozzle or diffuser vane being made by: · making a single-piece fiber blank (100; 400; 600; 800) by three-dimensional weaving; · shaping the fiber blank to obtain a single-piece fiber preform (200; 500; 700; 900) having a first portion forming an airfoil preform, a second portion forming an inner platform preform, and a third portion forming an outer platform preform; and · partially densifying the preform with a matrix to obtain a composite material vane having fiber reinforcement formed by the preform and densified by the matrix, and forming a single piece with inner and outer platforms incorporated therein; and • machining the vane, • assembling and bonding together a plurality of vanes to form a composite material multi-airfoil sector of a turbine nozzle or a compressor diffuser, the bonding being performed by a process including at least one step of bonding by co-densifying with a common matrix vanes that have already been assembled together while at an intermediate stage of densification. • making single-airfoil unit vanes (112; 412; 612; 812 1, 812 2) for a turbine nozzle or a compressor diffuser, each having an inner platform (114; 414; 614; 814a, 815a), an outer platform (116; 416; 616; 816a, 817a), and an airfoil extending between the inner and outer platforms and secured thereto, each nozzle or diffuser vane being made by: · making a single-piece fiber blank (100; 400; 600; 800) by three-dimensional weaving; · shaping the fiber blank to obtain a single-piece fiber preform (200; 500; 700; 900) having a first portion forming an airfoil preform, a second portion forming an inner platform preform, and a third portion forming an outer platform preform; and · partially densifying the preform with a matrix to obtain a composite material vane having fiber reinforcement formed by the preform and densified by the matrix, and forming a single piece with inner and outer platforms incorporated therein; and · making a single-piece fiber blank (100; 400; 600; 800) by three-dimensional weaving; · shaping the fiber blank to obtain a single-piece fiber preform (200; 500; 700; 900) having a first portion forming an airfoil preform, a second portion forming an inner platform preform, and a third portion forming an outer platform preform; and · partially densifying the preform with a matrix to obtain a composite material vane having fiber reinforcement formed by the preform and densified by the matrix, and forming a single piece with inner and outer platforms incorporated therein; and • machining the vane, • assembling and bonding together a plurality of vanes to form a composite material multi-airfoil sector of a turbine nozzle or a compressor diffuser, the bonding being performed by a process including at least one step of bonding by co-densifying with a common matrix vanes that have already been assembled together while at an intermediate stage of densification.