Nitrogen ions (N-2(+)) with 62 keV have been implanted into 100-nm-thick Ti films prepared by the evaporation on thermally cleaned NaCl substrates held at room temperature. The epitaxial growth process of resultant TiN films has been studied by transmission electron microscopy, Rutherford backscattering spectrometry, and elastic recoil;detection analysis. It has been revealed that the (110)-oriented TiNy is formed by nitriding the (110)-oriented TiHx in the as-deposited Ti film without change of the orientation of the fcc-Ti sublattice, and that the (001)-oriented TiNy and the "rotated" (110)-oriented TiNy rotated by similar to 9 degrees with respect to the (110)-oriented TIN,, respectively, are epitaxially formed by the transformation of (03.5)-oriented hcp-Ti to (001)-oriented fcc-Ti and by the transformation of (21.0)-oriented hcp-Ti to rotated (110)-oriented fcc-Ti. Then, the inheritance of the square atomic arrangement and parallelogram atomic arrangement of hcp-Ti plays a very prominent role in the epitaxy of the (001)-oriented and the rotated (110)-oriented TiNy, as well as the occupation of N in octahedral sites of the fcc-Ti. The increase in the lattice constants-of hcp-Ti, especially, the steeper increase of the lattice constant, c, by the N occupation can be considered as one of the driving forces for the hcp-fcc transformation. The growth mechanism of epitaxial TiNy films is discussed.