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The availability of low-index rutile TiO2 single crystal substrates with atomically flat surfaces is essential for enabling epitaxial growth of rutile transition metal oxide films. The high surface energy of the rutile (001) surface often leads to surface faceting, which precludes the sputter and annealing treatment commonly used for the preparation of clean and atomically flat TiO2(110) substrate surfaces. In this work, we reveal that stable and atomically flat rutile TiO2(001) surfaces can be prepared with an atomically ordered reconstructed surface already during a furnace annealing treatment in air. We tentatively ascribe this result to the decrease in surface energy associated with the surface reconstruction, which removes the driving force for faceting. Despite the narrow temperature window where this morphology can initially be formed, we demonstrate that it persists in homoepitaxial growth of TiO2(001) thin films. The stabilization of surface reconstructions that prevent faceting of high-surface-energy crystal faces may offer a promising avenue towards the realization of a wider range of high quality epitaxial transition metal oxide heterostructures. [ABSTRACT FROM AUTHOR]