We have studied relativistic ideal magnetohydrodynamical (MHD) winds in the stationary, axisymmetric magnetosphere of a rapidly rotating compact object without either gravitational or pressure effects. To obtain a highly accelerated wind, we expect that a plasma injected from a rapid rotator should pass smoothly through both the Alfven and fast magnetosonic points, where the poloidal velocity of the plasma equals either the Alfven-wave speed or that of a fast magnetosonic wave, it would blow with a large asymptotic fast-Mach number. For a pressure-free limit it has been widely believed that the fast magnetosonic point is located only at infinity. However, we show that an X-type fast magnetosonic point can exist at a finite distance. A super-fast MHD wind is allowed when a dense plasma starts to blow near the light surface with a sufficiently large energy. The predicted asymptotic velocity of the super-fast MHD wind can exceed the velocity of the widely known "Michel's minimum energy solution," which has been interpreted as giving the upper limit for the asymptotic flow velocity of winds.