Stability control for walking bipeds has been considered a complex task. Even two-dimensional fore-aft stability in dynamic walking appears to be difficult to achieve. In this paper we prove the contrary, starting from the basic belief that in nature stability control must be the sum of a number of very simple rules. We study the global stability of the simplest walking model by determining the basin of attraction of the Poincare´ map of this model. This shows that the walker, although stable, can only handle very small disturbances. It mostly falls, either forward or backward. We show that it is impossible for any form of swing leg control to solve backward falling. For the problem of forward falling, we devise a simple but very effective rule for swing leg action: "You will never fall forward if you put your swing leg fast enough in front of your stance leg. In order to prevent falling backward the next step, the swing leg shouldn't be too far in front." The effectiveness of this rule is demonstrated with our prototype "Mike.".