Quadrature spatial modulation (QSM) is a recently proposed multiple-input multiple-output transmission scheme which improves the spectral efficiency of classical spatial modulation (SM) by increasing the number of information bits transmitted by antenna indices. In QSM, a complex data symbol is decomposed into its real and imaginary components; then, these two components are independently transmitted using the SM principle. A low-complexity, near-maximum likelihood (ML) error performance achieving detection scheme is proposed for QSM to reduce the overall computational complexity of the ML detector. First, the proposed detector determines the set of most probable active transmit antennas and the corresponding possible transmission patterns. Then, ML-based detection is used to determine the transmitted complex data vector by performing a search over these transmission patterns and M-ary constellation symbols. It has been shown via computer simulations that the proposed detection algorithm exhibits near-ML bit error rate performance with considerably lower decoding complexity.