Understanding the underlying principles for the target-specific nuclease activity of CRISPR/Cas9 is a prerequisite to minimize its off-target DNA cleavage for genome engineering applications. Here, we show that the noncatalytic REC2 domain of Cas9 nuclease plays a crucial role in off-target discrimination. Using single-molecule fluorescence methods, we investigate conformational dynamics of the non-target strand (NTS) of DNA interacting with Cas9 and find that REC2 regulates the NTS rearrangement for cleavage reaction with the help of positively charged residues on its surface. This mechanistic model for the target specificity of Cas9 provides molecular insights for the rational approach to Cas9 engineering for highly specific genome editing.