In filter-bank multicarrier (FBMC) systems the intrinsic interference is the major challenge to achieve a full gain of diversity over multi-input multi-output (MIMO) channels. In this paper, we develop a novel multicarrier system called FBMC offset upper-lower polyphase network (FBMC/OULP) in which, to eliminate the intrinsic interference, the complex-valued symbols are alternatively transmitted via upper and lower half of polyphase network branches with an offset time. The symbol density of the FBMC/OULP system is equal to one complexvalued symbol in time-frequency lattice. Also, for transmission over frequency selective channels, a minimum mean square error (MMSE) estimator is employed at the receiver of the FBMC/OULP system to eliminate the interference caused by the frequency selectivity of the channel. The proposed scheme mitigates the produced interference between symbols in the upper and lower polyphase branches, based on the circular convolutional property. As a result of using complex-valued symbols and diminishing the interference, the full diversity gain of the orthogonal space-time block codes (OSTBC) can be achieved in MIMO channels by a low complex maximum likelihood (ML) detector. In comparison with the orthogonal frequency division multiplexing (OFDM) system, simulation results indicate that the proposed system achieves a superior performance in fast multi-path fading channels and a competitive performance in slow multi-path fading channels.