Hf70Cu25Rh5 and Hf70Cu25Ir5 amorphous alloys were prepared by a single roller melt-spinning method and the crystallization processes were studied by X-ray diffraction, differential scanning calorimetry and transmission electron microscopy. For both of the two alloys, the crystallization proceeds through the reactions of Am${\to}$I-phase${\to}$Hf2Cu+α-Hf, where Am and I-phase represent the amorphous and icosahedral quasicrystalline phases, respectively. Under optimum annealing conditions, the particle size of the I-phase is 10−25 and 10−20 nm for Rh- and Ir-containing alloys, respectively. Considering the fact that the crystallization process of Hf70Cu30 amorphous alloy does not accompany the precipitation of an I-phase, the present result demonstrates that the addition of Rh or Ir is significant. It is suggested that icosahedron-like atomic clusters exist in the amorphous state of Hf70Cu25Rh5 and Hf70Cu25Ir5 alloys, which serve as the seeds for the precipitation of the I-phase in the initial crystallization process.