The procedure consists of weaving on a loom two superimposed separate pieces of fabric, which are joined together transversally by weaving strands of warp at predetermined distances using strands of the weft, at the same time, in the direction of the warp independent bands with the corresponding hems in the longitudinal edges are formed in the loom, the sides of which are then subject to total or partial die cutting that conforms the bag or similar product. One of the fabrics to be used has, between the transversal and longitudinal hems, joining areas with floating strands of warp and joining areas with floating strands of weft, and this machine comprises means for moving, tensioning and aligning the fabric, and means for transversal and angular or curved cutting.