Bipedal robots can adapt to the urban environment of modern societies due to their particular locomotion mode similar to the human gait, and therefore, are good candidates for collaborating with humans by walking alongside them. However, motion planning while maintaining stability for these robots is a challenging issue that despite the development of new technologies and the advancement of knowledge, has not reached a satisfactory solution yet. In most of the methods proposed by researchers on the walking stability of bipedal robots, the general trend relies on ensuring an instantaneous stability by constraining the motion. Although those methods present good performance in sustaining stability, they lack to spare the robot a natural gait, often resulting in low efficiency strategies with high energy consumption. Consequently, some other walking techniques have been developed based on following a certain motion limit cycle, considering the overall stability of motion rather than satisfying it continuously. In this research, a method is proposed to preserve the stability of those limit cycles against disturbances. For this purpose, the dynamical model of the biped robot is extracted in the space of the mass center variables and, according to the desired step length and speed, a motion limit cycle is designed. Subsequently, a motion stabilizer is proposed based on the idea of step length shift, which is a natural human strategy for recovering the balance in case of sudden situation of disequilibrium. In order to alleviate the unwanted effects of proposed stabilizing strategy, a friction analysis helps to redesign the algorithm to a more advanced level of reliability. Ultimately, the motion stabilizer demonstrates its ability to withstand impacts, while taking into account the limitation of surface friction. As an extension, by defining a constrained optimization problem, the proposed stabilizer is implemented in the joint space. Finally, a simulation is performed on a biped robot model with realistic parameters, dealing with two different scenarios including impact during motion and in standstill position. The results show that this technique has a good performance in maintaining the stability of motion against impact, and exhibits responses similar to human reactions. Keywords: Biped Robot, Limit Cycle Walking, Push Recovery, Step Length Changing Strategy, Stability and non-slippage