Novel bisimidazole-containing peptidomimetic molecules, which can efficiently cleave RNA in the absence of divalent metal ions have been synthesized. The thymidine 5'-monophosphate derivatives modified with these peptidomimetics have been obtained on CPG (controlled pore glass) using a solid phase azide-alkyne cycloaddition. The ability of all synthesized derivatives to cleave RNA has been demonstrated by a solid-phase screening method. The resulting conjugates have provided a 20–100% cleavage of the RNA target in 18 hours. The results allow us to consider the described strategy as a useful approach for the rapid selection of potentially promising peptidomimetic molecules in order to synthesize reactive constructs on their basis.