A process for manufacturing a stiffener made of composite material with an inside surface of a concave shape, includes producing a flat strip (18) that includes at least one layer of fibers; heating it to be able to deform it; connecting one of the lateral edges of the strip (18) to a rotary mandrel (36) in such a way as to cause a winding of the strip on the mandrel (36) during its rotation, whereby the mandrel (36) has an outside surface (46) of which at least one part corresponds to the inside surface of the stiffener to be produced; and exerting tension at the other lateral edge of the strip (18) in a direction that is opposite to the direction of the movement of the strip (18) caused by the winding on the rotary mandrel (36).