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Gait recognition aims to identify individuals by recognizing their walking patterns. However, an observation is made that most of the previous gait recognition methods degenerate significantly due to two memorization effects, namely appearance memorization and label noise memorization. To address the problem, for the first time noisy gait recognition is studied, and a cyclic noise-tolerant network (CNTN) is proposed with a cyclic training algorithm, which equips the two parallel networks with explicitly different abilities, namely one forgetting network and one memorizing network. The overall model will not memorize the pattern unless the two different networks both memorize it. Further, a more refined co-teaching constraint is imposed to help the model learn intrinsic patterns which are less influenced by memorization. Also, to address label noise memorization, an adaptive noise detection module is proposed to rule out the samples with high possibility to be noisy from updating the model. Experiments are conducted on the three most popular benchmarks and CNTN achieves state-of-the-art performances. We also reconstruct two noisy gait recognition datasets, and CNTN gains significant improvements (especially 6% improvements on CL setting). CNTN is also compatible with any off-the-shelf backbones and improves them consistently.