The invention relates to a cap (1) that comprises a circular skirt (12), said cap including an irremovable portion (12-2) fixedly attached about the neck of a vessel (2) and a removable portion (12-1) removably attached to the neck, the irremovable and removable portions being separated by a first weakening line (20). In order to maintain the removable portion of the skirt attached to the irremovable portion of the skirt after the first opening, the skirt is provided with a second peripheral weakening line (34). It is also provided that the first weakening line extends less than 360°, while the two ends (34A, 34B) of the second weakening line are located along the periphery of the skirt respectively between a first (28A) of the two ends of a linking portion of the skirt and the hasp (26-1) closest to said first end, and between the second end (28B) of the linking portion and the hasp (26-6) closest to said second end.