Abstract: A tubular glove or insert having a front ring relief at one end and at an opposite end, an external ring relief. In an internal edge of the external ring relief are located two internal ring rows of teeth. A polyhedric tool is used to form a plurality of V-shaped cuttings or notches at equal distances in the internal surfaces of the external ring relief. The cuttings are then submitted to a further cutting or milling operation to form longitudinal slots centered at a vertex of the V-shaped notches at the back extremity of the V-shaped notches near the front ring relief so that the glove can be inserted into a connection body. This process allows the manufacturing of connection gloves (inserts) with a reduction in length and consequent reduction of material used and equipment used, as well as specialized manpower, while strengthening the grasping surface of the glove on a tube.