Abstract: A twist-off closure is disclosed for all kinds of containers having a head and a closure cap. The container head has at its top end a sealing lip shaped as a circumferential bead. A steep, multiple-start thread is located below the sealing lip. A fin is arranged between each winding of the steep thread and the container shoulder. The closure cap has a corresponding inner thread that co-operates in the closed state with the fins of the container head causing the closure cap to be clamped, so as to prevent the container from being unintentionally opened by itself. In the closed state, the first part of the windings of the thread of the closure cap engage the fins of the container head, and this is clearly perceived as a pressure point when twisting the cap by hand. All that is required to open and close the closure cap is to twist it through a half turn.