CCE1 is a DNA junction-resolving enzyme of Saccharomyces cerevisiae. Such enzymes are required to make two symmetrically paired cleavages in order to resolve the four-way junction productively. Using a cruciform assay, we show here that CCE1 introduces two unilateral cleavages in a sequential manner. This requires that the protein remains bound to the junction, preventing branch migration of the point of strand exchange. From a detailed kinetic analysis, we find that the CCE1 cleavage at a given site is accelerated by a factor of 5-10 when it occurs subsequently to the initial cleavage. These properties ensure a productive resolution of the four-way junction and may be general for junction-resolving enzymes.