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In this work, a new fast decoding technique that is based on dimensionality reduction for the search tree is presented for the high-rate space-time block coding. By the use of the proposed technique, the high-rate Golden codes and various WiMAX codes can be efficiently decoded with the optimal ML detection. In the sphere decoding algorithm, 8 dimensional search tree for 2 × 2 Golden code can be separated into 2 semi dependent, 6 dimensional sub trees. For the recommended X4 code in the WiMAX systems, 4 semi dependent, 5 dimensional sub trees can be obtained. By the proposed method, the computational complexity of the sphere decoding can be reduced by about %80 and the speed of the decoding can be increased about 5 times.