All-optical reswitching has been investigated in the half-metallic Heusler ferrimagnet , where Mn atoms occupy two inequivalent sites in the XA-type structure. The effect of a second 200 fs, 800 nm laser pulse that follows the first pump pulse, when both are above the threshold for switching, is studied as a function of , the time between them. Aims were to determine the minimum time needed for reswitching and to identify the physical mechanisms involved. The time trajectory of the switching process on a plot of sublattice angular momentum, vs , is in three stages; when , the sublattice moments are rapidly disordered, but not destroyed, while conserving net angular momentum via optical spin-wave excitations. This leads to transient parallel alignment of the residual Mn spins in the first quadrant. The net angular momentum associated with the majority sublattice then flips after about 2 ps, and a fully reversed ferrimagnetic state is then established via the spin-lattice interaction, which allows reswitching provided .