Fiberlike protrusions with a novel structure were found to grow on monocrystalline InP sputtered with 1-3 keV Ar+ at 100 degrees C. The fibers, which lengthened toward the incident ion beam, were of amorphous InP, except at the tip area receiving the highest ion-flux density. The tip area, including the growth front, was comprised of In and InP single crystals, the In crystals forming topotaxially in the core of the very tip. The crystallization at the tip of these fibers was no doubt attributable to the impact of Ar+ ions, so it may be termed a case of "ion-induced crystallization," which is an inverse process of the ion-induced amorphization of crystalline semiconductors.