In this study, a new high-rate generalized spatial modulation scheme is proposed for multiple-input multiple-output (MIMO) communications systems. In this scheme, two modulated symbols and the indices of the active two transmit antennas which are used in the transmission of these symbols are determined according to the incoming data bits. One of the data symbols is directly transmitted from a selected transmit antenna while the other one is transmitted from another selected transmit antenna with a rotation angle which is optimized for M-PSK signal constellations. The average bit error probability of the proposed system is analyzed for uncorrelated Rayleigh fading channels. It is shown via comprehensive computer simulations that the proposed high-rate generalized spatial modulation (HR-GSM) scheme provides significantly better error performance than classical SM, generalized SM (GSM), generalized spatial index modulation (GSIM) and quadrature SM (QSM) schemes.