Resistive switching memory, which is mostly based on polycrystalline thin films, suffers from wide distributions in switching parameters-including set voltage, reset voltage, and resistance-in their low- and high-resistance states. One of the most commonly used methods to overcome this limitation is to introduce inhomogeneity. By contrast, in this paper, we obtained uniform resistive switching parameters and sufficiently low forming voltage by maximizing the uniformity of an epitaxial thin film. To achieve this result, we deposited an SrFeOx/SrRuO3 heteroepitaxial structure onto an SrTiO3 (001) substrate by pulsed laser deposition, and then we deposited an Au top electrode by electron-beam evaporation. This device exhibited excellent bipolar resistance switching characteristics, including a high on/off ratio, narrow distribution of key switching parameters, and long data retention time. We interpret these phenomena in terms of a local, reversible phase transformation in the SrFeOx film between brownmillerite and perovskite structures. Using the brownmillerite structure and atomically uniform thickness of the heteroepitaxial SrFeOx thin film, we overcame two major hurdles in the development of resistive random-access memory devices: high forming voltage and broad distributions of switching parameters.