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Consider a flat-fading Multiple-Input Multiple-Output (MIMO) system. The near-optimum detection problematic has been shown to be efficiently solved through QR Decomposition (QRD)-based detectors. However, this step is demanding, and leads to wasting a large part of the system resource in case of a straightforward multi-carrier extension. In this paper, a solution that provides the QRD output by advantageously considering the correlation between adjacent channels is proposed. Originally, it relies on the matrix perturbation theory and induces a strong complexity reduction. Simulation results show that the proposed solution significantly reduces the implementation complexity while maintaining good performance.