In this paper, we extend the case of information exchange error mitigation for the distributed orthogonal space-time block code (DOSTBC) for two transmit antennas to distributed quasi-orthogonal space-time block code (DQOSTBC) for four transmit antennas. A rate 1 full-diversity DQOSTBC for four transmit antennas is designed. The code matrix changes according to different information exchange error cases, so full diversity is maintained even if not all information exchange is correct. We also perform analysis of the pairwise error probability. The performance analysis indicates that the proposed rate 1 DQOSTBC outperforms rate 1/2 DOSTBC for four transmit antennas at the same transmission rate, which is confirmed by the simulation results.