Homologous recombination involves the formation of branched DNA molecules that may interfere with chromosome segregation. To resolve these persistent joint molecules, cells rely on the activation of structure-selective endonucleases (SSEs) during the late stages of the cell cycle. However, the premature activation of SSEs compromises genome integrity, due to untimely processing of replication and/or recombination intermediates. Here, we used a biochemical approach to show that the budding yeast SSEs Mus81 and Yen1 possess the ability to cleave the central recombination intermediate known as the displacement loop or D-loop. Moreover, we demonstrate that, consistently with previous genetic data, the simultaneous action of Mus81 and Yen1, followed by ligation, is sufficient to recreate the formation of a half-crossover precursor in vitro. Our results provide not only mechanistic explanation for the formation of a half-crossover, but also highlight the critical importance for precise regulation of these SSEs to prevent chromosomal rearrangements.