We investigate the formation of self-organized InGaAs quantum wires (QWRs) on coherent multiatomic-stepped GaAs that had been grown on GaAs vicinal substrates by metal-organic vapor phase epitaxy. The key issues in the formation of InGaAs QWRs are the uniformity of the multiatomic steps and the large modulation in the lateral thickness of InGaAs on multiatomic-stepped GaAs structures. We use images obtained by atomic force microscopy and cross-sectional images of InGaAs layers obtained by transmission electron microscopy to investigate the surface morphology of InGaAs layers on multiatomic-stepped GaAs structures. As a result, we found that in the initial stages of InGaAs growth, Ga and In atoms preferentially attach themselves to the bottom edges of the multiatomic steps, and multiatomic-stepped structures with their own characteristic period and then reappear. These results suggest that the Schwoebel barrier, which causes the step bunching, may be decreased by the change of surface reconstruction after the introduction of small amount of In atoms to GaAs surfaces in the initial stage of growth. Furthermore, multiatomic-stepped structures formed during the growth of InGaAs layers have different periods from those on the underlying GaAs layer. The difference between the multiatomic-stepped structures on GaAs and InGaAs is thought to be caused by the difference of Schwoebel barriers between these two stepped surfaces.