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We investigate a multidimensional detection problem with a partial information of the a posteriori probability, which is referred to as the partial maximum a posteriori probability (MAP) detection problem. We show that the maximum likelihood (ML) detection of a higher dimension can be reduced to the ML detection of a lower dimension with cancellation under a certain condition through the formulation of the partial MAP detection problem. Using this, we can propose a computationally efficient algorithm to apply to the detection problem for multiple input multiple output (MIMO) channels including multiple transmit and multiple receive antenna (MTMR) channels and intersymbol interference (ISI) channels. It is shown that the proposed method has less error propagation effect, and its performance is close to that of the full ML detection with a lower computational complexity.