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In this paper, we propose a soft-input soft-output stack equalizer for multiple input multiple output (MIMO) frequency selective fading channels. In the literature, the soft or hard input/output stack algorithms to equalize single or multiple antenna time-invariant intersymbol interference (ISI) channels exist. After some modifications of the original sequential decoding metric, we show that the soft-input soft-output stack algorithm can be used at the receiver of the coded systems over frequency selective fading channels. Our examples illustrate that the proposed metrics result in promising near-optimum equalizers while offering a complexity independent of the memory of the channel.