We have designed an autocatalytic cycle based on the highly efficient 10-23 RNA-cleaving deoxyribozyme that is capable of exponential amplification of catalysis. In this system, complementary 10-23 variants were inactivated by circularization, creating deoxyribozymogens. Upon linearization, the enzymes can act on their complements, creating a cascade in which linearized species accumulate exponentially. Seeding the system with a pool of linear catalysts resulted not only in amplification of function but in sequence selection and represents an in vitro selection experiment conducted in the absence of any protein enzymes.