This paper presents a systematic method of the zigzag gait planning for quadruped walking robots. When a robot walks with a zigzag gait, its body is allowed to move from side to side, while the body movement is restricted along a moving direction in conventional continuous gaits. The zigzag movement of the body is effective to improve the gait stability margin. To plan a zigzag gait in a systematic way, the relationship between the center of gravity(COG) and the stability margin is firstly investigated. Then, new geometrical method is introduced to plan a sequence of the body movement which guarantees a maximum stability margin as well as monotonicity along a moving direction. Finally, an optimal swing-leg sequence is chosen for a given arbitrary configuration of the robot. To verify the proposed method, computer simulations have been performed for both cases of a periodic gait and a non-periodic gait.