The linear inverted pendulum model is often used to study walking gaits, but the transition from one step to the following step is often neglected, whereas it is really important for the walking stability. This letter studies different landing positions of the swing foot, and different conditions to switch the stance leg, based on time or on the configuration of the robot. It is shown that self-synchronization of the motion in sagittal and frontal planes is dependent on different switching conditions. Neither self-synchronization nor self-stabilization is observed when the stance leg switching is based on time or when both the step length and width are fixed. On the other hand, self-synchronization can be obtained when the switching condition of the stance leg is based on a linear combination of the positions of the center of mass (CoM) along the sagittal and frontal axes. Moreover, self-stabilization can be obtained when the velocity of the CoM in the sagittal plane is taken into account. Index Terms-Humanoid and bipedal locomotion, passive walking , dynamic stability.