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Recent attempts for unsupervised landmark learning leverage synthesized image pairs that are similar in appearance but different in poses. These methods learn landmarks by encouraging the consistency between the original images and the images reconstructed from swapped appearances and poses. While synthesized image pairs are created by applying pre-defined transformations, they can not fully reflect the real variances in both appearances and poses. In this paper, we aim to open the possibility of learning landmarks on unpaired data (i.e. unaligned image pairs) sampled from a natural image collection, so that they can be different in both appearances and poses. To this end, we propose a cross-image cycle consistency framework ($C^3$) which applies the swapping-reconstruction strategy twice to obtain the final supervision. Moreover, a cross-image flow module is further introduced to impose the equivariance between estimated landmarks across images. Through comprehensive experiments, our proposed framework is shown to outperform strong baselines by a large margin. Besides quantitative results, we also provide visualization and interpretation on our learned models, which not only verifies the effectiveness of the learned landmarks, but also leads to important insights that are beneficial for future research.