One of the advantages of legged locomotion over wheeled locomotion is that legged locomotion can tolerate much larger discontinuities in the terrain when compared to that of wheeled locomotion. In the absence of visual and/or distance measurement sensory feedback, the walking becomes an extra challenge if a priori knowledge of the terrain which is discontinuous is not available. One can imagine crossing over a stream by walking on rocks in dark. Obviously, the more legs there are, the easier it is to maintain static stability. In this paper, quadruped walking is considered. Briefly, the methodology presented in this paper is a search algorithm of a valid step which has to be in the conditioned manipulability ellipsoid given that the static stability is ensured. This is the necessary condition for a step to be valid. To be sufficient, the directional condition per desired trajectory has to be satisfied. We report our simulation results using 3 degrees-of-freedom per leg robot walking on beams in different height.