Cleaving of model RNA substrates by chemical ribonucleases constructed by conjugation of 1,4 diazabicyclo[2,2,2]octane with histamine and histidine was investigated. Similarly to RNase A, the chemical RNases produce fragments with 5' hydroxy-group and 3'-cyclophosphate. The cleavage occurs as the catalytic reaction: more than 150 phosphodiester bonds in RNA can be cleaved by one molecule of RNase mimic.