The double Holliday junction (dHJ) is generally regarded to be a key intermediate of meiotic recombination, whose resolution is critical for the formation of crossover recombinants. In fission yeast, the Mus81-Eme1 endonuclease has been implicated in resolving dHJs. Consistent with this role, we show that Mus81-Eme1 is required for generating meiotic crossovers. However, purified Mus81-Eme1 prefers to cleave junctions that mimic those formed during the transition from double-strand break to dHJ. Crucially, these junctions are cleaved by Mus81-Eme1 in precisely the right orientation to guarantee the formation of a crossover every time. These data demonstrate how crossovers could arise without forming or resolving dHJs using an enzyme that is widely conserved amongst eukaryotes.