In the last decade, there has been growing interests in studies aimed at delineating the strategies used by various nucleic acid enzymes to facilitate catalysis. Insights gained from such studies would enable the design of better DNA/RNA catalysts for various applications such as biosensing. DNA and RNA catalysts have been shown to be able to catalyze myriads of reactions, including peroxidation reactions, which are catalyzed by G-quadruplexes. In this report, we provide data that clarifies how G-quadruplex peroxidases achieve catalysis. Firstly, we show that by covalently linking a hemin cofactor to DNAzymes, anti-parallel G-quadruplexes, which have been previously shown to be catalytically inefficient, can be "resurrected" to become good peroxidation catalysts. We also reveal that the relative rates of peroxidation by DNAzyme peroxidases depend on the nature of the organic reductant, arguing for a special binding site in the peroxidase-mimicking DNAzymes for catalysis.