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By using joint modulation and a customized constellation set, we show that quasi-orthogonal space-time block coding (QO-STBC) can be used to form a new differential space-time modulation (DSTM) scheme to provide full transmit diversity with non-coherent detection. Our new scheme can provide a higher code rate than existing DSTM schemes based on orthogonal STBC. It also has a lower decoding complexity than other DSTM schemes, such as those based on group codes, because it only requires a joint detection of two complex symbols. We derive the design criteria for the customized constellation set and use them to construct a constellation set that provides a wide range of spectral efficiency with full diversity and maximum coding gain.