•Treatment of InSb (001) substrate with 1M aqueous Na2S solution results in nearly complete removal of native oxides.•A sulfide protective layer formed by the S-treatment is desorbed at much lower temperatures than the native oxide layer.•The bulk InSb epilayers grown on the S-treated substrates have very smooth surface (RMS ∼0.1nm).•Good structural quality of the homointerfaces formed at the S-treated substrates is confirmed by TEM. The aqueous sodium sulfide solution has been used for pre-epitaxial preparation of epi-ready InSb (001) substrates for molecular beam epitaxy (MBE) of InSb layers. X-ray photoemission spectroscopy study shows that the S-treated surface of InSb (001) substrate generally does not contain a native oxide layer and is covered with a sulfide protecting overlayer. Atomic-force microscopy and transmission electron microscopy have been applied to compare surface topography and structural properties of InSb layers grown by MBE on S-treated and untreated epi-ready InSb (001) substrates. The MBE growth of InSb layers with very smooth surface possessing the root-mean-square roughness as low as 0.1nm and good structural quality has been demonstrated on the S-treated substrates.