Abstract: The invention relates to an improved sole for footwear with a convex or rounded shape, provided with a stabilizer, with a damping system and with an internal system for the rotation of air, which modifies the phase of contact of the foot with the ground in a roller, such that it transforms the process of reception of the ground (with the heel of the foot) and forward translation of the propelling forces (by means of the area of the metatarsus and toes) in a roller effect, obtaining the damping/stability/impulse effects, and the actuation of the airing system by means of a pad/wedge, the outsole thus configured allowing a rotation on the ground such that the inertia of the body and the vertical forces applied from the heel of the foot are more easily converted into horizontal propelling forces.