According to the invention, the section (2) comprises a double-sided adhesive strip (8) which is covered with a protective film (11). The aforementioned protective film (11) is removed by way of a pull tab (12) before gluing, the tab consisting of two tab parts (15) which are positioned on either side of a slit (16) in the film. The automated method comprises, in the extrusion line, a step whereby the pull tab (12) is joined to the adhesive-covering protective film in the middle of the adhesive area transversely to the section. The tab and the protective film are subsequently cut in order to produce two tab parts which are each connected to the end of one length of protective film (18) which is intended to be torn off. The invention is particularly suitable for use in the car industry and in building and for producers and users of extruded sections which are glued using double-sided adhesive.