In this paper, a new multiple-input multiple-output (MIMO) modulation scheme termed as fully-quadrature spatial modulation (F-QSM) is proposed. The F-QSM is a class of space modulation techniques (SMTs) that harness the spatial positions of the transmit antennas in the transmit antenna array to fulfill high data rates. However, the data rates of most of SMTs are restricted to be logarithmically proportional to the number of transmit antennas. This logarithmic proportion is considered a pivotal crisis of most of SMTs, as it bottlenecks the enhancement in their data rates with the increment in the number of transmit antennas. Accordingly, the proposed F-QSM vanquishes this crisis by using a novel transmission mechanism to acquire a linear proportion between the achievable data rate and number of transmit antennas. This linear proportion, enables the proposed F-QSM to achieve a higher data rate than the conventional SMTs and by using a lower number of transmit antennas. In this paper, a mathematical framework for assessing the average bit error rate (ABER) performance of the proposed F-QSM is investigated thoroughly. Moreover, the receiver computational complexity of the proposed F-QSM is evaluated and tested reference to the computational complexity of the conventional SMTs at different number of transmit antennas. Simulation results reveal the effectiveness of the analytical analysis and corroborate the surpass of the proposed F-QSM in terms of ABER performance and achievable data rate at the expense of increasing receiver computational complexity compared to the conventional SMTs.