The invention relates to a milking member for an animal. The milking member comprises a claw (1), a plurality of teat cups (3a-d), a plurality of milk conduits (2a-d), which each is connected to the claw (1) at a first end and to a teat cup (3a-d) at a second end, and means, which makes it possible to hold the respective teat cups (3a-d) in a substantially upright positions on a level above the claw (1) when the milking member not is attached to an animal. Said means comprises milk conduits (2a-d), which have a stiffness such that they are able to hold the respective teat cups (3a-d) in said upright positions on a level above the claw (1) when the teat cups (3a-d) not are attached to the teats of an animal.