Recently, it has been proved that a different switching surface can preserve the walking trajectory while varying the walking stability [1], [2]. In this paper, by employing the simplest passive dynamic biped, we optimize the switching surface to maximize the robot's stability. Here, the stability measure is preferably the size of the basin of attraction, i.e. the collection of all possible initial conditions leading to the system's equilibrium point. Numerical investigations indicate that the maximum stability is obtained for neither the highest nor the lowest walking speed.