In this paper, we propose a differential space-time modulation (DSTM) scheme for multiple input multiple output (MIMO) systems with 2, 4, and 8 transmit antennas. This scheme is used for MIMO systems where the channel coefficients are not available at both the transmitter and the receiver. For 2 transmit antennas, the transmission matrices are selected from Weyl group. We use the Kronecker product of matrices of the Weyl group to design new groups for the schemes using 4 and 8 transmit antennas. Simulation results show the performance of these schemes.