As electrons are injected at various energies into ferromagnetic material with their spin polarization vector perpendicular to the axis of the magnetization, we observe precessional motion of the spin polarization on the femtosecond time scale. Because of angular momentum conservation, the magnetization vector must process as well. We show that spin injection will generate the precessional magnetization reversal in nanosized ferromagnetic bits. At reasonable injected current densities this occurs on the picosecond time scale.