Abstract—This paper proposes a new differential super-quasiorthogonal space-time trellis codes (SQOSTTC) with singlesymbol maximum-likelihood (ML) decoding. Firstly, a new joint constellation, which can be used to construct a unitary matrix for quasi-orthogonal space-time block code (QOSTBC), is designed. Secondly, based on the joint constellation and criterion of maximizing the coding gain distance (CGD), set-partitioning is done. Finally, we introduce the simple single-symbol maximumlikelihood (ML) decoding. Simulation results show that our differential SQOSTTC can get better performance than the differential super-orthogonal space-time trellis code (SOSTTC) [5] with four transmit antennas at the transmission rate of