InN was epitaxially grown on (0001) α-Al2O3 substrates by the halogen transport method. Surface treatment of the substrate by a H2+Br2 gas (passed over In) just before the growth was essential for obtaining the epitaxial layers of InN. Arrays of extra spots were observed in the reflection electron-diffraction patterns of thin InN films. The extra spot arrays could be explained from the viewpoint that the crystal film was composed of twins. In these twin structures, the twinning planes were (7̄ 12 5̄ 0) and (1̄ 1̄ 20 9̄ 0). These extra spots ultimately disappeared with prolonged growth time. This result shows that as the growth proceeds, crystallites having a predominant orientation overwhelm other crystallites.