Employing passive dynamics of the simplest point-foot walker, we have shown that the walking surface could have a great role in promoting the gait stability. In this regard, the stabilization of the simplest walking model,3 between the range of slopes greater than 0.0151 rad. and less than 0.26 rad., has been achieved. The walker like other passive dynamic walking models has no open or closed-loop control system; so, is only actuated by the gravity field. Moreover, no damper or spring is used. Obviously, according to the model's unstable behavior, it is unable to walk on an even flat ramp between the mentioned intervals.3 Here, instead of restraining the model, we let it explore other smooth surfaces, walking on which, will end in an equally inclined surface. To reach the objective, we employ a parallel series of fixed straight lines (local slopes) passing through contact points of an unstable cycling gait, which is generated by an ordinary ramp. To categorize, we have nicknamed those local slopes that guide the biped to a stable cyclic walking, “Ground Attractors,” and the other, leading it to a fall, “Repulsive Directions.” Our results reveal that for the slope <0.26 rad., a closed interval of ground attractors could be found. Stabilization of those unstable limit cycles by this technique makes obvious the key role of walking surface on bipedal gait. Furthermore, following our previous work,13 the results confirm that the two thoroughly similar walking trajectories can have different stability. All of these results strongly demonstrate that without considering the effects of a walking surface, we cannot establish any explicit relationship between the walker's speed and its stability.