The Combined Fission Matrix (CFM) method entails the instantaneous estimation of the entire system's fission matrix by amalgamating fission matrices from a pre-existing database. This approach allows for the rapid and accurate determination of the effective multiplication factor (keff) and the distribution of fission rates across the reactor system. This work applies the CFM method to the Japan Research Reactor-3 (JRR-3M), a water-cooled plate-type reactor. The CFM method demonstrates a high level of agreement with Monte Carlo (MC) simulation results, completing calculations within a minute. In the two cases of 'All Absorbers In' and 'All Absorbers Out', this method achieved a low root-mean-square (RMS) error of only 0.4% and 1% , respectively, with keff-error of 44 pcm and 24 pcm .