The invention relates to a milking unit comprising a milk collection part and at least two milk tubes that are connected to the milk collection part. At least one end of the milk tube has an essentially spherical clamping body, the central point of the clamping body being offset in relation to the longitudinal axis (S) of the milk tube and/or the clamping body having a channel with a mouth. The longitudinal axis (S) penetrates a plane, on which the cross-sectional surface of the mouth lies at an angle that is not equal to 90°.
