A method of fabricating a complex part out of composite material including three-dimensional woven fiber reinforcement densified by a matrix, the method including three-dimensionally weaving a continuous fiber strip including a succession of fiber blanks for preforms of a plurality of parts that are to be fabricated; subsequently cutting individual fiber blanks out from the strip, each blank being a one-piece blank; shaping a cut-out blank to obtain a one-piece fiber preform having a shape that is close to the shape of a part that is to be fabricated; consolidating the preform in the desired shape; and densifying the consolidated preform by forming a matrix by chemical vapor infiltration.