Lattice-matched (Delta a/a=0.09%) ScAlMgO4(0001) substrates were employed to grow single crystalline quality ZnO films by laser molecular-beam epitaxy. Extremely smooth surface represented by atomically flat terraces and half unit cell (0.26 nm) high steps and extremely small orientation fluctuations both in-plane (< 0.02 degrees) and out-of-plane (< 0.01 degrees) are achieved. The films have high mobility (similar to 100 cm(2)/V s) together with low residual carrier concentration (similar to 10(15) cm(-3)). Excellent optical properties, including a clear doublet of A and B exciton peaks in absorption spectra, were also observed. These features could not be simultaneously achieved for ZnO films grown on sapphire(0001) having a large lattice mismatch (Delta a/a=18%).