DNA catalysts are fundamental building blocks for diverse molecular information-processing circuits. Allosteric control of DNA catalysts has been developed to activate desired catalytic pathways at desired times. Here we introduce a new type of DNA catalyst that we call a cooperative catalyst: a pair of reversible reactions are employed to drive a catalytic cycle in which two signal species, which can be interpreted as an activator and an input, both exhibit catalytic behavior for output production. We demonstrate the role of a dissociation toehold in controlling the kinetics of the reaction pathway and the significance of a wobble base pair in promoting the robustness of the activator. We show near-complete output production with input and activator concentrations that are 0.1 times the gate concentration. The system involves just a double-stranded gate species and a single-stranded fuel species, as simple as the seesaw DNA catalyst, which has no allosteric control. The simplicity and modularity of the design make the cooperative DNA catalyst an exciting addition to strand-displacement motifs for general-purpose computation and dynamics.