A closure piece (1) for a medical syringe is provided, the syringe having a syringe barrel (3) and a syringe neck (23). The closure piece has an adapter (6) which can be fitted onto the syringe neck (23). A screw-type closure piece (4) can be fitted onto the adapter (6). A twist-off ring (13) is connected to the screw-type closure piece (4). A closure cap (5) can be introduced into the syringe neck (23).