Two synthetically modified nucleoside triphosphate analogues (adenosine modified with an imidazole and uridine modified with a cationic amine) are enzymatically polymerized in tandem along a degenerate DNA library for the combinatorial selection of an RNAse A mimic. The selected activity is consistent with both electrostatic and general acid/base catalysis at physiological pH in the absence of divalent metal cations. The simultaneous use of two modified nucleotides to enrich the catalytic repertoire of DNA-based catalysts has never before been demonstrated and evidence of general acid/base catalysis at pH 7.4 for a DNAzyme has never been previously observed in the absence of a divalent metal cation or added cofactor, This work illustrates how the incorporation of protein-like functionalities in nucleic acids can bridge the gap between proteins and oligonucleotides underscoring the potential for using nucleic acid scaffolds in the development of new materials and improved catalysts for use in chemistry and medicine.