Metal-dependent nucleases that generate double-strand breaks in DNA often possess two symmetrically-equivalent subunits, arranged so that the active sites from each subunit act on opposite DNA strands. Restriction endonuclease BfiI belongs to the phospholipase D (PLD) superfamily and does not require metal ions for DNA cleavage. It exists as a dimer but has at its subunit interface a single active site that acts sequentially on both DNA strands. The active site contains two identical histidines related by 2-fold symmetry, one from each subunit. This symmetrical arrangement raises two questions: first, what is the role and the contribution to catalysis of each His residue; secondly, how does a nuclease with a single active site cut two DNA strands of opposite polarities to generate a double-strand break. In this study, the roles of active-site histidines in catalysis were dissected by analysing heterodimeric variants of BfiI lacking the histidine in one subunit. These variants revealed a novel mechanism for the scission of double-stranded DNA, one that requires a single active site to not only switch between strands but also to switch its orientation on the DNA.