Differential spatial modulation (DSM) is able to transmit additional data bits without increasing the number of radio-frequency chains and power consumption and also avoids pilot overhead. In this paper, we propose two new schemes of DSM to improve the original DSM. One is an increased-rate scheme that transmits one additional data bit per two blocks. The bit mapping and maximum-likelihood detection is particularly designed. The goal of the second scheme is to increase the diversity of DSM. By properly designing block coded modulation and complex antenna-index matrices, the proposed scheme can achieve the desired diversity order. Compared with the existing schemes with the same constellation of the transmitted signals, the proposed scheme achieves higher transmission rates.