The RecQ DNA helicases, human BLM and yeast Sgs1, form a complex with topoisomerase III (Top3) and are thought to act during DNA replication to restart forks that have paused due to DNA damage or topological stress. We have shown previously that yeast cells lacking SGS1 or TOP3 require MMS4 and MUS81 for viability. Here we show that Mms4 and Mus81 form a heterodimeric structure-specific endonuclease that cleaves branched DNA. Both subunits are required for optimal expression, substrate binding, and nuclease activity. Mms4 and Mus81 are conserved proteins related to the Rad1–Rad10 (XPF/ERCC1) endonuclease required for nucleotide excision repair (NER). However, the Mms4–Mus81 endonuclease is 25 times more active on branched duplex DNA and replication fork substrates than simple Y-forms, the preferred substrate for the NER complexes. We also present genetic data that indicate a novel role for Mms4–Mus81 in meiotic recombination. Our results suggest that stalled replication forks are substrates for Mms4–Mus81 cleavage—particularly in the absence of Sgs1 or BLM. Repair of this double-strand break (DSB) by homologous recombination may be responsible for the elevated levels of sister chromatid exchange (SCE) found in BLM−/− cells.