In this paper, we propose a new spatial modulation (SM) scheme based on quaternary quasi-orthogonal sequences (Q-QOSs), referred to as Q-QOS-SM. First, the conventional SM and generalized-SM (GSM) schemes are reinterpreted as a new transmission scheme based on a spatial modulation matrix (SMM), whose column indices are used for the mapping of spatial-information bits unlike the conventional ones. Next, by adopting the SMM comprising the Q-QOSs, the proposed Q-QOS-SM that guarantees twice the number of spatial bits at a transmitter compared with the SM with a constraint of transmit antennas, is designed. From the computer-simulation results, the Q-QOS-SM is shown to achieve a greatly improved throughput compared with the conventional SM and GSM schemes, especially, for a large number of the receive antennas. This finding is mainly because the new scheme offers a much higher minimum Euclidean distance than the other schemes.