A tidy pet litter box having a plurality of internal screens across which the pet must traverse when entering or leaving a main basin of the litter box. An upper lid fits over a lower tray, the upper lid having a large front opening. The lower tray defines a large main basin in which litter is placed, and a secondary basin at a rear end thereof. An entrance screen mounted laterally across side walls of the upper lid extends from a lower end of the front opening substantially over the entire main basin and permits passage of a pet to a rear screen located above the secondary basin. To exit, the pet must jump up to the rear screen, then over the entrance screen which dislodges any litter sticking to its paws so that it falls back into the main basin. A method of training a cat to use the litter box by first removing the entrance screen is also disclosed.
