The invention relates to a method for making a composite part including an assembly of superimposed webs of reinforcement threads imbedded at least partially in a polymer matrix, said part including at least one curved area and the method comprising steps of draping or stacking plies of a composite material, characterized in that, in at least one area adjacent to a curved area, at least one draping or stacking step is carried out with a ply of composite material, that comprises a web, or twisted thread web, including at least one twisted reinforcement thread in order to at least compensate the length differences of the extreme paths of the thread on either side of the width as measured in a direction parallel to the surface of the web; the invention also relates to the composite materials thus obtained.