We report here the structure of BstYI, an "intermediate" type II restriction endonuclease with overlapping sequence specificities to BamHI and BglII. BstYI, a thermophilic endonuclease, recognizes and cleaves the degenerate hexanucleotide sequence 5'-RGATCY-3' (where R=A or G and Y=C or T), cleaving DNA after the 5'-R on each strand to produce four-base (5') staggered ends. The crystal structure of free BstYI was solved at 1.85A resolution by multi-wavelength anomalous dispersion (MAD) phasing. Comparison with BamHI and BglII reveals a strong structural consensus between all three enzymes mapping to the alpha/beta core domain and residues involved in catalysis. Unexpectedly, BstYI also contains an additional "arm" substructure outside of the core protein, which enables the enzyme to adopt a more compact, intertwined dimer structure compared with BamHI and BglII. This arm substructure may underlie the thermostability of BstYI. We identify putative DNA recognition residues and speculate as to how this enzyme achieves a "relaxed" DNA specificity.