In this paper we deal with the presence of the intrinsic intersymbol interference (ISI) in the filter-bank multicarrier systems. Indeed, the received data symbols are accompanied by interference terms, which complicate the detection in a maximum likelihood (ML) sense in the spatial multiplexing scheme. Detection schemes with ISI estimation and cancellation are not always effective due to the error propagation. We propose a receiver based on a partial ISI cancellation followed by the Viterbi detector. A simple tentative detector is first used to cancel partially the ISI. We show that under some conditions the ISI cancellation is effective and the performance converges to the optimum one.