Homing endonucleases are unusual enzymes, capable of recognizing lengthy DNA sequences and cleaving site-specifically within genomes. Many homing endonucleases are encoded within group I introns, and such enzymes promote the mobility reactions of these introns. Phage T4 has three group I introns, within the td, nrdB and nrdD genes. The td and nrdD introns are mobile, whereas the nrdB intron is not. Phage RB3 is a close relative of T4 and has a lengthier nrdB intron. Here, we describe I-TevIII, the H-N-H endonuclease encoded by the RB3 nrdB intron. In contrast to previous reports, we demonstrate that this intron is mobile, and that this mobility is dependent on I-TevIII, which generates 2-nt 3' extensions. The enzyme has a distinct catalytic domain, which contains the H-N-H motif, and DNA-binding domain, which contains two zinc fingers required for interaction with the DNA substrate. Most importantly, I-TevIII, unlike the H-N-H endonucleases described so far, makes a double-strand break on the DNA homing site by acting as a dimer. Through deletion analysis, the dimerization interface was mapped to the DNA-binding domain. The unusual propensity of I-TevIII to dimerize to achieve cleavage of both DNA strands underscores the versatility of the H-N-H enzyme family.