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We analyze the bit error rate (BER) performance of M-ary quadrature amplitude modulation (M-QAM) when using space-time block coding (STBC) along with packet combining triggered by automatic repeat request (ARQ) retransmission over multiple-input multiple-output (MIMO) fading channels. Specifically, adopting a log-likelihood ratio (LLR) based approach and considering the 16-QAM case of study, we provide an exact formulation for the aggregate LLR distribution in the case the STBC codeword can be transmitted twice, and derive the resulting BER. For higher number of retransmissions, an approximation of the error function is used to derive the LLR distributions and the system's ensuing BER. Considering different values of combined transmissions and M-QAM with possible constellation rearrangement (CoRe), validation of the proposed BER analytical model through simulations and assessment of the advantages of packet combining are provided for transmissions over additive white Gaussian noise (AWGN) channel and orthogonalized MIMO Rayleigh fading channels with different STBC mappings.