In this paper, we propose a new mathematical group called the Extended Weyl group aiming at increasing the spectral efficiency of the conventional Differential Space-Time Modulation (DSTM) found in literature. More specifically, the paper aims at solving the problem of spectral efficiency decrease of DSTM when the number of transmit antennas of Multiple-Input Multiple-Output (MIMO) systems increases. Moreover, this work proposes a thorough analysis of the distance spectrum between DSTM matrices and adopts a near optimal matrices mapping to decrease the bit error probability. The analysis and simulation results show clearly the improvement and outperformance of the adopted strategies.