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This paper presents an efficient design of the block adaptive frequency-domain equalization (FDE) for space-time block-coded (STBC) single-carrier system with the cyclic-prefix. We propose a weighted STBC-like matrix-wise block adaptive FDE (STBC-BFDE). In the STBC-BFDE, the STBC-like matrix-wise block is first formulated for the receive blocks. The correction terms of the equalizer coefficients in each block are then calculated in a weighted least-square (LS) sense that the weighted squared norm of the a posteriori error vector is minimized. An approximate steady-state excess mean-square error (EMSE) of the STBC-BFDE for the stationary optimal coefficient is also analyzed. From the theoretical analysis, it is shown that the EMSE decreases as the STBC-like matrix-wise block length increases. Simulation results also show in a time-varying typical urban (TU) channel that the bit-error-rate (BER) performances of the STBC-BFDE are improved as the STBC-like matrix-wise block length increases.