A method for manufacturing a preform for producing a part made of composite material with an unchangeable final shape includes supplying a triaxial non-woven textile comprising a layer of fibers orientated in a first direction, a layer of fibers orientated in a second direction, a layer of fibers orientated in a third direction, and seams extending parallel to each other and forming sheaths for the circumferential fibers, arranging the textile on an element of unchangeable shape by placing the seams parallel to the circumferential direction of the element, and sliding the circumferential fibers into the sheaths so that the textile is in continuous contact with the element.