We propose use of QR decomposition with sort and Dijkstra's algorithm for decreasing the computational complexity of the sphere decoder that is used for ML detection of signals on the multi-antenna fading channel. QR decomposition with sort decreases the complexity of search part of the decoder with small increase in the complexity required for preprocess part of the decoder. Dijkstra's algorithm decreases the complexity of searching part of the decoder with increase in the storage complexity. The computer simulation demonstrates that the complexity of the decoder is reduced by the proposed methods significantly.