Enzyme systems containing a single subunit and requiring only magnesium for endonucleolytic activity. The corresponding modification methylases are separate enzymes. The systems recognize specific short DNA sequences and cleave either within, or at a short specific distance from, the recognition sequence to give specific double-stranded fragments with terminal 5'-phosphates. Enzymes from different microorganisms with the same specificity are called isoschizomers. EC 3.1.21.4.