A general and simple differential modulation scheme that can be applied to both partial-diversity quasi-orthogonal space-time block codes and full-diversity quasi-orthogonal space-time block codes is reported. A new class of quasi-orthogonal coding structures is presented for various number of transmit antennas. Differential encoding and decoding can be simplified to differential Alamouti codes by grouping the signals in the transmitted matrix and decoupling the detection of data symbols, respectively. For the codes with partial transmit diversity, the new scheme can achieve constant amplitude of transmitted signals, and avoid signal constellation expansion; in addition, it has a linear signal detector with very low complexity. Simulation results show that these partial-diversity codes can provide very useful results at low signal-to-nose ratio for current communication systems. For codes with full transmit diversity achieved by constellation rotation, the proposed scheme has performance equal to the best full-rate quasi-orthogonal schemes previously described in the literature with the benefit of a simpler detector. Moreover, a simple linear detector is also presented for the case when two orthogonal ASK constellations are used. Extension to more than four transmit antennas is also considered.