In this paper, an instant gait stability measure is proposed applicable to dynamic gaits as well as static gaits of quadruped walking robot. The gait stability measure is obtained from the angular momentum of the system about the supporting edges in a support polygon in the quadrupedal gait, also the swing leg is considered in defining the gait stability measure. The validity of the proposed gait stability measure is examined and discussed along with the gait stability analyses for several representative gait parameters using the proposed dynamic model.