Most of the time, humans do not watch their steps when walking, especially on even grounds. They walk without thinking. How robust is this strategy? How rough can the terrain be to walk this way? Walking performance depends on the dynamical contribution of each part of the body. While it is well known that the head is stabilized during the motions of humans and animals, its contribution to walking equilibrium remains unexplored. To address the question we operate, in simulation, a simplified walking model. We show that the introduction of a stabilized head-neck system drastically improves the robustness to ground perturbations. It significantly influences the dynamics of walking and hence to the balance. Our study is a starting point of a wider research on the involvement of vertebral limbs in the mechanics and control of the human steady gait. It also studies the benefits of such simple control schemes capable to produce complex behaviors.