The decomposition of methanol-d4 that was adsorbed on Au-Rh bimetallic nanoclusters grown by the sequential deposition of Au and Rh vapors onto ordered thin-film Al2O3/NiAl(100) at 300 K, occurred by means of dehydrogenation and primarily on the surface Rh. Nevertheless, the surface Rh atoms were not equally reactive; their reactivity altered with both structural and electronic effects arising from the alloying. The Au deposited on Rh clusters decorated the surface and deactivated Rh by not only directly obstructing them but also by neighboring them. As the initially incorporated Au tended to aggregate around reactive low-coordinated Rh atoms, such as corner Rh atoms, the reactivity of the cluster, indicated by the CO and deuterium (D2) produced per surface Rh, decreased markedly. In contrast, the Rh deposited on Au clusters promoted their reactivity. The reactivity was sharply enhanced by a few incorporated Rh atoms, as they preferentially decorated the edge Au atoms, resulting in their lower coordination, more positive charge, higher energetic d-band centers, and high reactivity. On the reactive Rh, the scission of the O-D bond in the initial dehydrogenation of methanol-d4 became more preferential than the competing desorption. The further incorporated Rh failed to promote the reactivity, but the clusters remained more reactive than those formed by Rh clusters incorporating Au as their structuring involved an active atomic segregation that yielded more low-coordinated and reactive surface Rh.