Milking device for milking a dairy animal, comprising at least one teat cup (1), wherein the teat cup (1) comprises a flexible cup liner (4) around a teat space, and a single pulsation space (3) and a milk line (10), a milking vacuum pump (12) connected to the milk line, for providing a milking vacuum, a pulsator (9) connected to the pulsation space (3), for providing a controllable air pressure in the pulsation space (3), and a control device (13) for controlling at least the pulsator during at least a milking action. The milking device has been improved owing to the fact that the control device (13) is configured to cause the pulsator and/or the milking vacuum pump (12) to provide, in a period of time consecutive to a milking action wherein a dairy animal is milked and a teat (6) is located in the teat space, such a substantially stable, non-pulsating pressure difference between the pulsation space (3) and the teat space, that the cup liner (4) shuts off the teat space from the milk line (10).
