We prepared L1(0)-ordered FeNi alloy films by alternate deposition of Fe and Ni monatomic layers, and investigated their magnetic anisotropy. We employed a non-ferromagnetic Au-Cu-Ni buffer layer with a flat surface and good lattice matching to L1(0)-FeNi. An L1(0)-FeNi film grown on Au6Cu51Ni43 showed a large uniaxial magnetic anisotropy energy (K-u = 7.0 x 10(6) erg cm(-3)). K-u monotonically increased with the long-range order parameter ( S) of the L1(0) phase. We investigated the Fe-Ni composition dependence by alternating the deposition of Fe 1 - x and Ni 1 + x monatomic layers ( -0.4 < x < 0.4). Saturation magnetization (M-s) and K-u showed maxima (M-s = 1470 emu cm(-3), K-u = 9.3 x 10(6) erg cm (-3)) for Fe60Ni40 (x = -0.2) while S showed a maximum at the stoichiometric composition (x = 0). The change in the ratio of lattice parameters (c/a) was small for all compositions. We found that enrichment of Fe is very effective to enhance Ku. The large Ms and Ku of Fe60Ni40 indicate that Fe-rich L10-FeNi is promising as a rare-earth-free permanent magnet.