How to reduce the hardware cost and high power consumption of RF link of communication device is the key problem to be solved for multi-transmitting antenna and multi-receiving antenna system (MIMO). Always choose the best antennas connection a limited number of RF circuits, which is called antenna selection technology (AS), are a perfect solution to the problem, Assuming that the spatial range of the antenna meets the requirements of signal multiplexing and based on the maximum capacity criterion of the selected MIMO system, the manuscript proposes a low computational complexity (CC) and high performance joint transmitting and receiving antenna selection technique (JTRAS). Starting from the traditional capacity formula and the full matrix of MIMO channel, we utilize a simplified channel capacity expression through repeatedly iterating to delete a row and a column of the equivalent decrement channel matrix, which is to remove a pair of transmitting and receiving antennas. Based on the decreasing JTRAS (DJTRAS) algorithm, the capacity results of simulating calculation indicate that its median capacity overtakes other ones, such as optimum selection (OS), AS based on Frobenius 2 norm (NBS), and concise joint AS criterion (CJAS) etc., and the novel DJTRAS scheme can significantly reduce computational complexity (CC) compared to the exhaustive search method with maximum capacity, which defined as optimal algorithm in the curve graphs. This new technology of the AS is particularly suited to large number of selected antennas, such as Lt ≥ NT/2,Lr ≥ NR/2.