In this thesis, a new turning gait is proposed for a quadruped walking robot. The proposed scheme makes it possible to control the translation and orientation of the walking robot simultaneously. More specifically, an analytic approach is employed to find feasible gaits which guarantee positive longitudinal stability margin for a desired movement of translation and rotation of the walking robot. The lifting time of each leg is then analytically computed for a feasible gait. A method for selecting an optimal gait among feasible gaits is suggested for some typical tasks for a given quantity of translation and rotation. From the viewpoint of stability, the proposed turning gait shows better performance than wave gait. The proposed turning gait has been implemented for the walking robot KAISER II, and verified to be practical.