Genome editing by Cas9, which cleaves double-stranded DNA at a sequence programmed by a short single-guide RNA (sgRNA), can result in off-target DNA modification that may be detrimental in some applications. To improve DNA cleavage specificity, we generated fusions of catalytically inactive Cas9 and FokI nuclease (fCas9). DNA cleavage by fCas9 requires association of two fCas9 monomers that simultaneously bind target sites ∼15 or 25 base pairs apart. In human cells, fCas9 modified target DNA sites with >140-fold higher specificity than wild-type Cas9 and with an efficiency similar to that of paired Cas9 'nickases', recently engineered variants that cleave only one DNA strand per monomer. The specificity of fCas9 was at least fourfold higher than that of paired nickases at loci with highly similar off-target sites. Target sites that conform to the substrate requirements of fCas9 occur on average every 34 bp in the human genome, suggesting the versatility of this approach for highly specific genome-wide editing.