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For iterative detection and decoding (IDD) in multiple-input multiple-output (MIMO) systems, the MIMO detector needs to provide soft-decisions. Since the complexity of the maximum a posteriori probability (MAP) detector grows exponentially with the number of transmit antennas, various suboptimal detectors are proposed to exploit the tradeoff between complexity and performance. Among them, the minimum mean square error (MMSE)-soft cancellation (SC) detector has an excellent tradeoff. In this paper, by noting that the MMSE-SC detector is an approximate MAP detector, another approximate MAP detector that uses successive processing is proposed. The proposed successive detector can provide a better performance than the MMSE-SC detector, while its complexity is comparable with that of the MMSE-SC detector. An interesting feature of the proposed successive detector is that the tradeoff between complexity and performance can be exploited by a single parameter, which could be an important control parameter in practical implementations.