Reflection high-energy electron diffraction (RHEED) has been used to study the epitaxial growth of GaAs on GaAs. Ordered arrays of steps were observed on both the singular and vicinal surfaces. The surfaces were prepared by chemically etching and then heating to 900 K to drive off the oxide. The evolution of the RHEED pattern was then followed for growth conditions given with respect to a nonequilibrium phase diagram showing the various surface reconstructions observed for GaAs (001). Specifying growth conditions in this fashion eliminates instrumental uncertainties. The utility of RHEED for the determination of the step distribution is described and demonstrated.