The invention relates to a system for cleaning a carcass part of slaughtered poultry, which carcass part at least still comprises a part of the breast fillet and skin, which skin comprises at least a part of the breast skin, neck skin and skin in the region of transition between the breast skin and neck skin, wherein the breast skin and the skin in the region of transition between the breast skin and neck skin rest at least partly against the muscular tissue of the breast fillet, from which carcass part the muscular tissue of the neck and the neck vertebrae are substantially removed, which system comprises a neck skin removing device which comprises: a gripper for engaging a part of the neck skin that is connected to the rest of the carcass or carcass part, a stretching station, which stretching station is configured to exert a force on the neck skin engaged by the gripper in such a way that the skin in the region of transition between the breast skin and neck skin is stretched and becomes detached from the muscular tissue of the breast fillet, a blade which is adapted to cut into or to cut through the stretched skin in the region of transition between the breast skin and neck skin while the neck skin in the stretching station is subjected to the force.