This paper presents a multi-group independent sub-channels allocation precoding (MGISAP) algorithm for multi-group space-time coding (MGSTC) systems in correlated high frequency Multiple Input Multiple Output (HF-MIMO) channels. In this algorithm, we jointly consider singular value decomposition (SVD) and optimization of grouping and power allocation to increase the robustness in correlated fading channels. Using SVD method, the original MIMO channel is divided into independent multiple sub-channels. Then, we group the sub-channels and allocate their power optimally. Each group transmit space-time coding signal parallelly and independently so that the robustness in correlated fading channels is improved. Mathematical analysis and simulation results verify the outstanding performance of the proposed algorithm.