Domain diversity between different datasets poses an evident challenge for adapting the person re-identification (Re-ID) model trained on one dataset to another. State-of-the-art unsupervised domain adaptation methods for person Re-ID optimize the pseudo labels created by clustering algorithms on the target domain; however, the inevitable label noise caused by the clustering procedure is ignored. Such noisy pseudo labels substantially hinder the model's ability to further improve feature representations on the target domain. To address this problem, this study proposes a mutual teaching approach for unsupervised domain adaptation of person Re-ID based on relation-aware attention (RAA) and local feature relearning (FRL). For feature extraction, we employ multi-channel attention to capture the corresponding local features of a person and use spatial-channel correspondence to relearn discriminative fine-grained details of global and local features; thereby, enhancing the network's feature representation capabilities. We also use RAA to steer the two networks toward different feature regions to enhance their distinctiveness and complementarity. Extensive experiments were conducted on public datasets to validate the proposed method. The experimental results show that the proposed method performs well in multiple-person Re-ID tasks.