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Cleaning the surface of InSb from oxides is an important step in epitaxial growth and post-growth technological processes, since the oxide layer leads to the formation of defects in epitaxial layers and degradation of device parameters. It is shown that cleaning the InSb surface from oxides by annealing in an indium flux reduces the maximum annealing temperature and surface roughness compared to thermal annealing in vacuum: the root mean square roughness of the InSb surface is found to be 1.2 nm after cleaning by annealing in vacuum at 400 °C and 0.9 nm after cleaning by annealing in an indium flux at 355 °C followed by annealing in vacuum at 380 °C. The lower surface roughness of the InSb substrates after the cleaning step improves the crystal quality of the grown epitaxial layers. Based on the in-situ monitoring of oxide desorption by high energy electron diffraction, it is shown that the antimony flux slows down the indium oxide desorption process, which leads to the necessity of increasing the maximum annealing temperature.