A claw (C) for a milking machine comprises an enclosure having an upper part (1) and a lower part (2) and enclosing an inner space (3) for a milk flow during a milking operation. A centre axis (x) extends through the enclosure and through the upper part and the lower part. The upper part comprises an upper end (5) defining an upper end point, and a lower annular end (7) extending along a periphery of the claw in a connection plane (p). The lower part is detachably connected to the upper part along the connection plane, and rotary symmetric with respect to an axis (χ') of rotation being perpendicular to the connection plane. The connection plane is inclined with respect to the centre axis so that the enclosure have a first height at a first peripheral position (p i ) and a second height at a second peripheral position (P 2 ) diametrically opposite to the first peripheral position, and that the first height is greater than the second height.