Deoxyribozymes that ligate RNA expand the scope of nucleic acid catalysis and allow preparation of site-specifically modified RNAs. Previously, deoxyribozymes that join a 5'-hydroxyl and a 2',3'-cyclic phosphate were identified by in vitro selection from random DNA pools. Here, the alternative strategy of in vitro evolution was used to transform the 8-17 deoxyribozyme that cleaves RNA into a family of DNA enzymes that ligate RNA. The parent 8-17 DNA enzyme cleaves native 3'-5' phosphodiester linkages but not 2'-5' bonds. Surprisingly, the new deoxyribozymes evolved from 8-17 create only 2'-5' linkages. Thus, reversing the direction of the DNA-mediated process from ligation to cleavage also switches the selectivity in forming the new phosphodiester bond. The same change in selectivity was observed upon evolution of the 10-23 RNA-cleaving deoxyribozyme into an RNA ligase. The DNA enzymes previously isolated from random pools also create 2'-5' linkages. Therefore, deoxyribozyme-mediated formation of a non-native 2'-5' phosphodiester linkage from a 5'-hydroxyl and a 2',3'-cyclic phosphate is strongly favored in many different contexts.