Multivalent recognition and binding of biological molecules is a natural phenomenon that increases the binding stability (avidity) without decreasing the recognition specificity. In this study, we took advantage of this phenomenon to increase the efficiency and maintain high specificity of RNA cleavage by DNAzymes (Dz). We designed a series of DNA constructs containing two Dz agents, named here bivalent Dz devices (BDD). One BDD increased the cleavage efficiency of a folded RNA fragment up to 17-fold in comparison with the Dz of a conventional design. Such an increase was achieved due to both the improved RNA binding and the increased probability of RNA cleavage by the two catalytic cores. By moderating the degree of Dz agent association in BDD, we achieved excellent selectivity in differentiating single-base mismatched RNA, while maintaining relatively high cleavage rates. Furthermore, a trivalent Dz demonstrated an even greater efficiency than the BDD in cleaving folded RNA. The data suggests that the cooperative action of several RNA-cleaving units can significantly improve the efficiency and maintain high specificity of RNA cleavage, which is important for the development of Dz-based gene knockdown agents.