DNA-cleaving restriction enzymes are well-known tools in biomedical and biotechnological research. There are, however, no corresponding enzymes known for RNA cleavage. There has been an ongoing development of artificial ribonucleases, including some attempts at sequence selectivity. However, so far these systems have displayed modest rates of cleavage, and in most cases, the cleaver has been used in excess or in stoichiometric amounts. In the current work, we present PNA-based systems (PNAzymes) that carry a Cu(II)-2,9-dimethylphenanthroline group and that act as site and sequence specific RNases. The general basis for the systems is that the target is cleaved at a nonbase paired region (RNA bulge) which is formed in the substrate upon binding of the PNAzyme. With this copper based system, cleavage takes place at virtually only one site and with a half-life of down to 30 min under stoichiometric conditions. Efficient turnover of RNA-substrate is shown with a 100-fold excess of substrate, thus, demonstrating true enzyme behavior. In addition, alteration of the sequence in the RNA bulge or a mismatch in the base-pairing region leads to substantial decreases in rate showing both kinetic resolution and binding discrimination in the substrate selectivity. The selectivity is further demonstrated by the substrates, with two potential cleavage sites differing in only one base, are cleaved only at the site that either does not have a mismatch or is kinetically preferred. We suggest that these systems can serve as a basis for construction of RNA restriction enzymes for in vitro manipulations.