In this paper, we present a novel unpaired point cloud completion network, named Cycle4Completion, to infer the complete geometries from a partial 3D object. Previous unpaired completion methods merely focus on the learning of geometric correspondence from incomplete shapes to complete shapes, and ignore the learning in the reverse direction, which makes them suffer from low completion accuracy due to the limited 3D shape understanding ability. To address this problem, we propose two simultaneous cycle transformations between the latent spaces of complete shapes and incomplete ones. The insight of cycle transformation is to promote networks to understand 3D shapes by learning to generate complete or incomplete shapes from their complementary ones. Specifically, the first cycle transforms shapes from incomplete domain to complete domain, and then projects them back to the incomplete domain. This process learns the geometric characteristic of complete shapes, and maintains the shape consistency between the complete prediction and the incomplete input. Similarly, the inverse cycle transformation starts from complete domain to incomplete domain, and goes back to complete domain to learn the characteristic of incomplete shapes. We provide a comprehensive evaluation in experiments, which shows that our model with the learned bidirectional geometry correspondence outperforms state-of-the-art unpaired completion methods.