We have investigated the processes of Au-In alloy formation in Au/InSb(111)A system by using TED (transmission electron diffraction) and HR-TEM (high-resolution transmission electron microscopy) in the plan-view and profile geometries. At room temperature, the Au₉In₄ alloy with a γ-brass structure emerges on the InSb(111)A surface with an Au coverage of 3 ML. Subsequent annealing at 150^oC leads to the structural and stoichiometric changes from Au₉In₄ to AuIn₂ that fits the substrate better than Au₉In₄ (0.6% for AuIn₂ and 1.3% for Au₉In₄). Such changes are promoted by In-rich conditions and high mobility of In atoms induced by high temperature annealing.