A novel concept to improve the catalytic functions of nucleic acids (DNAzymes) is introduced. The method involves the conjugation of a DNA recognition sequence (aptamer) to the catalytic DNAzyme, yielding a hybrid structure termed "nudeoapzyme". Concentrating the substrate within the "nudeoapzyme" leads to enhanced catalytic activity, displaying saturation kinetics. Different conjugation modes of the aptamer/DNAzyme units and the availability of different aptamer sequences for a substrate provide diverse means to design improved catalysts. This is exemplified with (i) The H2O2-mediated oxidation of dopamine to aminochrome using a series of hemin/G-quadruplex-dopamine aptamer nudeoapzymes. All nudeoapzymes reveal enhanced catalytic activities as compared to the separated DNAzyme/aptamer units, and the most active nudeoapzyme reveals a 20-fold enhanced activity. Molecular dynamics simulations provide rational assessment of the activity of the various nudeoapzymes. The hemin/G-quadruplex aptamer nudeoapzyme also stimulates the chiroselective oxidation of L- vs D-DOPA by H2O2. (ii) The H2O2-mediated oxidation of N-hydroxy-D-arginine to D-citrulline by a series of hemin/G-quadruplex arginine aptamer conjugated nudeoapzymes.