Genetic recombination arises during meiosis through the repair of DNA double-strand breaks (DSBs) that are created by Spo11, a topoisomerase-like protein1,2. Spo11 DSBs form preferentially in nucleosome-depleted regions termed hotspots3,4, yet how Spo11 engages with its DNA substrate to catalyse DNA cleavage is poorly understood. Although most recombination events are initiated by a single Spo11 cut, here we show in Saccharomyces cerevisiae that hyperlocalized, concerted Spo11 DSBs separated by 33 to more than 100 base pairs also form, which we term 'double cuts'. Notably, the lengths of double cuts vary with a periodicity of 10.5 base pairs, which is conserved in yeast and mice. This finding suggests a model in which the orientation of adjacent Spo11 molecules is fixed relative to the DNA helix-a proposal supported by the in vitro DNA-binding properties of the Spo11 core complex. Deep sequencing of meiotic progeny identifies recombination scars that are consistent with repair initiated from gaps generated by adjacent Spo11 DSBs. Collectively, these results revise our present understanding of the mechanics of Spo11-DSB formation and expand on the original concepts of gap repair during meiosis to include DNA gaps that are generated by Spo11 itself.