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Non-parallel voice conversion (VC) is a technique for learning mappings between source and target speeches without using a parallel corpus. Recently, cycle-consistent adversarial network (CycleGAN)-VC and CycleGAN-VC2 have shown promising results regarding this problem and have been widely used as benchmark methods. However, owing to the ambiguity of the effectiveness of CycleGAN-VC/VC2 for mel-spectrogram conversion, they are typically used for mel-cepstrum conversion even when comparative methods employ mel-spectrogram as a conversion target. To address this, we examined the applicability of CycleGAN-VC/VC2 to mel-spectrogram conversion. Through initial experiments, we discovered that their direct applications compromised the time-frequency structure that should be preserved during conversion. To remedy this, we propose CycleGAN-VC3, an improvement of CycleGAN-VC2 that incorporates time-frequency adaptive normalization (TFAN). Using TFAN, we can adjust the scale and bias of the converted features while reflecting the time-frequency structure of the source mel-spectrogram. We evaluated CycleGAN-VC3 on inter-gender and intra-gender non-parallel VC. A subjective evaluation of naturalness and similarity showed that for every VC pair, CycleGAN-VC3 outperforms or is competitive with the two types of CycleGAN-VC2, one of which was applied to mel-cepstrum and the other to mel-spectrogram. Audio samples are available at http://www.kecl.ntt.co.jp/people/kaneko.takuhiro/projects/cyclegan-vc3/index.html.