In this contribution an algorithm for joint detection in fast frequency hopping/multiple frequency shift keying (FFH/MFSK) multiple access (MA) systems is presented. The new algorithm - referred to as REC algorithm - evaluates ambiguities which occur during the decision process and iteratively reduces the number of candidate symbols. The REC algorithm is of low complexity, suitable for every addressing scheme, and effective for both an interference-only channel and a fading channel. For the interference-only channel the REC algorithm enables maximum likelihood (ML) joint detection with low computational effort.