BNx films with N content varying from 2 to 40 at. % were deposited by dual ion beam deposition. The films are solid admixtures of a B-rich phase composed of icosahedral atomic clusters, and a graphite-like boron nitride phase. The fraction of the B-rich phase drops, while that of the graphite-like boron nitride phase grows with increasing N content. The hardness of the films first rises, reaches a maximum value of 18.8 GPa at a N content of 20.2 at, %, and falls with further increase in N content. This rise is explained by assuming that some N atoms are located interstitially at the sites surrounded by icosahedral clusters, such that the hardness of the material is enhanced as a result of additional cross-linking of the network by the N atoms. However, the overall N contents are not sufficient to ensure the two phases to have the ideal stoichiometry of B4N and hexagonal BN (h-BN) structures, so that the B-rich phase in the film does not exhibit the theoretical strangest possible cross-linking that has been proposed for the ideal B4N structure. The drop in the hardness of the films with N contents exceeding 20.2 at. % arises from the increasing volume fraction of the graphite-like boron nitride phase.