Homologous recombination proceeds via the formation of several intermediates including Holliday junctions (HJs), which are important for creating crossover products. DNA strand exchange is a core reaction that produces these intermediates that is directly catalyzed by RecA family recombinases, of which there are two types in eukaryotes: universal Rad51 and meiosis-specific Dmc1. We demonstrated previously that Rad51 promotes four-strand exchange, mimicking the formation and branch migration of HJs. Here we show that Dmc1 from fission yeast has a similar activity, which requires ATP hydrolysis and is independent of an absolute requirement for the Swi5-Sfr1 complex. These features are critically different from three-strand exchange mediated by Dmc1, but similar to those of four-strand exchange mediated by Rad51, suggesting that strand exchange reactions between duplex-duplex and single-duplex DNAs are mechanistically different. Interestingly, despite similarities in protein structure and in reaction features, the preferential polarities of Dmc1 and Rad51 strand exchange are different (Dmc1 promotes exchange in the 59-to-39 direction and Rad51 promotes exchange in the 39-to-59 direction relative to the ssDNA region of the DNA substrate). The significance of the Dmc1 polarity is discussed within the context of the necessity for crossover production.