The invention relates to a method and an apparatus for minimizing or even avoiding the transfer of an infection from an infected teat/quarter udder to a healthy teat. The invented method for cleaning the teats (9) of a dairy animal's udder is controlled by a robot means (6) for carrying and operating a cleaning means (8, 14) to clean said teats (9) in succession. This is accomplished by first cleaning one or more healthy teat(s), and then cleaning one or more teat(s) being subjected to various levels of infection. The invented apparatus for cleaning the teats of a dairy animal's udder comprises a control unit (1), a cleaning means (8, 14), a robot means (6) controlled by the control unit (1), a robot arm (7) arranged on the robot means (6) to carry and operate the cleaning means (8, 14) so as to clean the dairy animal's teats in succession.