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Unsupervised domain adaptation (UDA) for person re-identification is challenging because of the huge gap between the source and target domain. A typical self-training method is to use pseudo-labels generated by clustering algorithms to iteratively optimize the model on the target domain. However, a drawback to this is that noisy pseudo-labels generally cause trouble in learning. To address this problem, a mutual learning method by dual networks has been developed to produce reliable soft labels. However, as the two neural networks gradually converge, their complementarity is weakened and they likely become biased towards the same kind of noise. This paper proposes a novel light-weight module, the Attentive WaveBlock (AWB), which can be integrated into the dual networks of mutual learning to enhance the complementarity and further depress noise in the pseudo-labels. Specifically, we first introduce a parameter-free module, the WaveBlock, which creates a difference between features learned by two networks by waving blocks of feature maps differently. Then, an attention mechanism is leveraged to enlarge the difference created and discover more complementary features. Furthermore, two kinds of combination strategies, i.e. pre-attention and post-attention, are explored. Experiments demonstrate that the proposed method achieves state-of-the-art performance with significant improvements on multiple UDA person re-identification tasks. We also prove the generality of the proposed method by applying it to vehicle re-identification and image classification tasks. Our codes and models are available at https://github.com/WangWenhao0716/Attentive-WaveBlock.