SummarySpatial Modulation (SM) is a technology that incorporates digital modulation and coding with multiple antennas to achieve high data rates along with improved energy efficiency. Quadrature spatial modulation (QSM), which extends the transmitted signals to in‐phase and quadrature domains, has recently been proposed to improve spectral efficiency (SE) for SM. In this paper, we have considered a combination of Generalized QSM (GQSM) and Quasi Orthogonal Space Time Block Codes (QOSTBC). We propose a new detection scheme for the GQSM and use three different prevailing detection schemes for QOSTBC. We present Bit Error Rate (BER) versus average SNR performance for the combined system using M‐QAM constellations with quasi‐static spatially uncorrelated Rayleigh fading channels and computational complexity in terms of numbers of addition/multiplication and search time. We have compared the considered system with prevailing GQSM system and shown that the prevailing system, as per active antenna permutation (AAP) in GQSM, offers number of transmitted bits ranging from 2 to 9 whereas the proposed system offers number of transmitted bits ranging from 6 to 16 in the same bandwidth. Thus, there is a visible gain in SE. Furthermore, we have compared the BER performance of the considered system with the performance of maximum likelihood detector (MLD) and spatial modulation (SM). In the considered system, the QOSTBC improves the diversity gain. Hence, we have shown that the considered Scheme 3 substantially outperforms the SM. Further, the considered system with Scheme 3 has nearly similar BER performance with the maximum likelihood detector (MLD), which has higher computational complexity.