The invention relates to a method for producing a transmission shaft (1) comprising a body (2) made from composite and a coupling piece (3) at one end of the body (2), said coupling piece (3) being hollow and having splines (4) on the inner surface thereof, the base (6) of the splines (4) delimiting the perimeter of a circle of diameter D2 and the head (5) of the splines (4) delimiting the perimeter of a circle of diameter D1, characterized in that said method comprises the successive steps of: providing a mandrel (10) having an expandable part (12) and a non-expandable part (11); producing the body (2) by winding pre-impregnated fiber filaments around the mandrel (10); positioning the coupling piece (3) around the body (2) on the expandable part (12) of the mandrel; expansion of the expandable part (12) of the mandrel (10) in order to fill the base (6) of the splines (4) with the impregnated fibers of the body (2); curing the body (2) provided with the coupling piece (3).