We characterize the class of strategy proof and efficient two-sided matching mechanisms which are “gender-neutral” in the sense that they treat the two sides of the mechanism equitably. All such mechanisms can be implemented by an algorithm which matches agents in a sequence of steps. Each step selects one agent from each side. These two agents are either matched together or are matched with their most-preferred remaining partner from the other side. We establish a connection between one and two-sided matching which enables our characterization.