Asynchronous digital circuits working in military and space environments are often subject to the adverse effects of radiation faults. In this paper, we propose a new hardening technique against radiation faults. The considered digital system has the structure of DMR (Double Modular Redundancy), in which two sub-systems conduct the same work simultaneously. Based on the output feedback, the proposed scheme diagnoses occurrences of radiation faults and realizes immediate recovery to the normal behavior by overriding parts of memory bits of the faulty sub-system. As a case study, the proposed control scheme is applied to an asynchronous dual ring counter implemented in VHDL code.