Thin-film growth of alkali halides on (001) surfaces of fcc transition metals was studied using reflection high-energy electron diffraction. Alkali halide grew with its [100] axis rotated by 45degrees from that of the metal substrate ([100](film)//[110](substrate)) for LiCl/Cu(001) and LiCl/Ni(001). On the contrary, alkali halide grew without azimuthal rotation ([100](film)//[100](substrate)) for LiCl/Ag(001), NaCl/Cu(001), NaCl/Ag(001), and NaCl0.6Br0.4/Ag(001). The former growth mode ([100](film)//[110](substrate)) occurred only with a small difference in the first-nearest neighbor (first-NN) interatomic distance between alkali halide and metal. The latter growth mode ([100](film)//[100](substrate)) occurred even with a large difference in the first-NN interatomic distance. The mechanism of the latter growth was explained by the preferential direction of steps on (001) surfaces of fcc metals and the migration of alkali halide molecules to the steps.