An in vitro evolution procedure was used to obtain RNA enzymes with a particular catalytic function. A population of 10(13) variants of the Tetrahymena ribozyme, a group I ribozyme that catalyzes sequence-specific cleavage of RNA via a phosphoester transfer mechanism, was generated. This enzyme has a limited ability to cleave DNA under conditions of high temperature or high MgCl2 concentration, or both. A selection constraint was imposed on the population of ribozyme variants such that only those individuals that carried out DNA cleavage under physiologic conditions were amplified to produce "progeny" ribozymes. Mutations were introduced during amplification to maintain heterogeneity in the population. This process was repeated for ten successive generations, resulting in enhanced (100 times) DNA cleavage activity.