Fast human walking includes a phase where the stance heel rises from the ground and the stance foot rotates about the stance toe. This phase where the biped becomes underactuated is not present during the walk of current humanoid robots. The objective of this study is to determine whether the introduction of this phase for a 3-D bipedal robot is useful to reduce the energy consumed in the walking. In order to study the efficiency of this new gait, two cyclic gaits are presented. The first cyclic motion is composed of successive single-support phases with a flat stance foot on the ground, and the stance foot does not rotate. The second cyclic motion is composed of single-support phases that include a subphase of rotation of the supporting foot about the toe. The single-support phases are separated by a double-support phase. For simplicity, this double-support phase is considered as instantaneous (passive impact). For these two gaits, optimal motions are designed by minimizing the torques cost. The given performances of actuators are taken into account. It is shown that, for a fast motion, a foot-rotation subphase is useful to reduce the cost criterion. These gaits are illustrated with simulation results.