The RNA-guided CRISPR-Cas9 nuclease from Streptococcus pyogenes (SpCas9) has been widely repurposed for genome editing1-4. High-fidelity (SpCas9-HF1) and enhanced specificity (eSpCas9(1.1)) variants exhibit substantially reduced off-target cleavage in human cells, but the mechanism of target discrimination and the potential to further improve fidelity are unknown5-9. Here, using single-molecule Frster resonance energy transfer experiments, we show that both SpCas9-HF1 and eSpCas9(1.1) are trapped in an inactive state10 when bound to mismatched targets. We find that a non-catalytic domain within Cas9, REC3, recognizes target complementarity and governs the HNH nuclease to regulate overall catalytic competence. Exploiting this observation, we design a new hyper-accurate Cas9 variant (HypaCas9) that demonstrates high genome-wide specificity without compromising on-target activity in human cells. These results offer a more comprehensive model to rationalize and modify the balance between target recognition and nuclease activation for precision genome editing.