A technology was developed for molybdenum-99 recovery from the fuel of the Argus solution reactor of the National Research Center, Kurchatov Institute (NRC KI). The technology was tested with simulated solutions and actual samples of irradiated fuel of the Argus solution reactor. The fundamental efficiency of the developed method has been demonstrated. Yield of Mo-99 extracted from the solution reactor fuel is more than 0.90, and within the entire process scheme (two stages of sorption and two stages of desorption) Mo-99 yield is 0.70. The results of analysis of molybdenum-99 obtained in the NRC KI, as well as in the third-party organizations (IPPE SRC RF, the Belgian Institute of Radioelements in Fleurus and at Argonne National Laboratory) indicate that in terms of all the monitored parameters it amply meets the international requirements for radiochemical purity.