The invention relates to a local connection of top and bottom sheets (1, 2) onto one another in their contact surface (11) in at least one defined connection zone (3), whereby this zone (3) is polygonal and whereby within the periphery of this zone (3) the top and bottom sheets (1) and (2) jointly form a connecting lip (12) with their first side faces (5, 6) located opposite one another cut obliquely through their sheet thickness. These first side faces (5, 6) of the sheets (1, 2) and their adjacent obliquely-oriented second side faces (8, 9) in the zone (3) are complementarily bevelled in the form of a conical wall running downwards and inwards, so that in the vicinity of these second neighbouring side faces (8, 9) the underside (7) of the bottom sheet (2) protrudes inwards past the top surface (4) of the connecting lip (12) at the location of the top outside edges (13) of its first side faces (5, 6). The invention also comprises a method and apparatus to implement this connection.