Building on previous propositions to generate walking gaits online through the use of Linear Model Predictive Control, the goal of this paper is to show that it is possible to allow on top of that a continuous adaptation of the positions of the foot steps, allowing the generation of stable walking gaits even in the presence of strong perturbations, and that this additional adaptation requires only a minimal modification of the previous schemes, especially maintaining the same Linear Model Predictive form. Simulation results are proposed then on the HRP-2 humanoid robot, showing a significant improvement over the previous schemes.