A new decoding algorithm that consists of two decoding stages to reduce the complexity of the maximum likelihood decoding for parallel combinatory high-compaction multi-carrier modulation is presented. The first decoding stage is in charge of a preliminary decision that coarsely searches the candidates using the QRD-M algorithm, and the second decoding stage is responsible for the final decision that recovers the message data using the candidates chosen in the first decoding stage. The proposed two-stage decoding algorithm is shown to be effective with respect to bit-error rate performance, with a small increase in computational complexity, compared to the one-stage decoding using the QRD-M algorithm.