This paper proposes out-of-bound signal demapping for lattice reduction-aided iterative linear receivers in overloaded MIMO channels. While lattice reduction aided linear receivers sometimes output hard-decision signals that are not contained in the modulation constellation, the proposed demapping converts those hard-decision signals into binary digits that can be mapped onto the modulation constellation. Even though the proposed demapping can be implemented with almost no additional complexity, the proposed demapping achieves more gain as the linear reception is iterated. Furthermore, we show that the transmission performance depends on bit mapping in modulations such as the Gray mapping and the natural mapping. The transmission performance is confirmed by computer simulation in a 6 × 2 MIMO system, i.e., the overloading ratio of 3. One of the proposed demapping called “modulo demapping” attains a gain of about 2 dB at the packet error rate (PER) of 10^-1 when the 64QAM is applied.