Epitaxial ZnO thin films were grown by laser molecular-beam epitaxy on lattice-matched ScAlMgO4 substrates following the deposition and annealing of suitable buffer layers. The samples were characterized by low-temperature photoluminescence (PL), absorption, and reflectivity measurements. PL from higher order (n=2) excitons (A exciton) was observed at temperatures lower than 40 K. The absorption spectrum contained lines and the reflection spectrum exhibited anomalies that were assigned to the excited-states (n=2,3) of A and B excitons. The optical quality could be improved dramatically by using annealed ZnO or MgZnO buffer layers.