One of the recently modified multiple-input multiple-output (MIMO) systems is the spatial modulation (SM). Although SM is considered as MIMO in its composition, a single antenna at the transmitting side is activated at any time instant. Among all transmitting antenna, the selection of this active antenna isn't random but rather chosen based on extra bits, called spatial bits, transmitted besides the conventional digitally modulated bits. In addition to the transmission of additional bits, SM wireless communication system achieves an enhanced power efficiency, low error rate, low complexity at receiver, and completely inter-channel interference (ICI) elimination. On the other side, SM suffers from the dramatic increase in the number of required transmit antennas to achieve a small improvement in data rate and low spectral efficiency when compared with multiplexing MIMO (Mux-MIMO). The logarithmic increase in the data rate of the SM scheme became linear thanks to the fully generalized spatial modulation scheme (F-Gen-SM). Although the F-Gen-SM scheme overcame one of the SM disadvantages, the achievable data rate still low when compared with Mux-MIMO. Grouping generalized spatial modulation scheme (Gr-Gen-SM) tries to find a compromise between the advantage of SM and the high spectral efficiency of Mux-MIMO. Gr-Gen-SM achieves high spectral efficiency but loses most of the SM advantages. This paper introduces a new F-Gen-SM scheme utilizing the idea of dividing transmit antennas into groups (F-Gr-Gen-SM). This proposed scheme provides an improvement on data rate while preserving the advantages of SM as much as possible.