The formation of crossovers is a fundamental genetic process. The XPF-family endonuclease Mus81-Mms4 (Eme1) contributes significantly to crossing over in eukaryotes. A key question is whether Mus81-Mms4 can process Holliday junctions that contain four uninterrupted strands. Holliday junction cleavage requires the coordination of two active sites, necessitating the assembly of two Mus81-Mms4 heterodimers. Contrary to this expectation, we show that Saccharomyces cerevisiae Mus81-Mms4 exists as a single heterodimer both in solution and when bound to DNA substrates in vitro. Consistently, immunoprecipitation experiments demonstrate that Mus81-Mms4 does not multimerize in vivo. Moreover, chromatin-bound Mus81-Mms4 does not detectably form higher-order multimers. We show that Cdc5 kinase activates Mus81-Mms4 nuclease activity on 3' flaps and Holliday junctions in vitro but that activation does not induce a preference for Holliday junctions and does not induce multimerization of the Mus81-Mms4 heterodimer. These data support a model in which Mus81-Mms4 cleaves nicked recombination intermediates such as displacement loops (D-loops), nicked Holliday junctions, or 3' flaps but not intact Holliday junctions with four uninterrupted strands. We infer that Mus81-dependent crossing over occurs in a noncanonical manner that does not involve the coordinated cleavage of classic Holliday junctions.