Completing an unordered partial point cloud is a challenging task. Existing approaches that rely on decoding a latent feature to recover the complete shape, often lead to the completed point cloud being oversmoothing, losing details, and noisy. Instead of decoding a whole shape, we propose to decode and refine a lowresolution (low-res) point cloud first, and then performs a patch-wise noise-aware upsampling rather than interpolating the whole sparse point cloud at once, which tends to lose details. Regarding the possibility of lacking details of the initially decoded low-res point cloud, we propose an iterative refinement to recover the geometric details and a symmetrization process to preserve the trustworthy information from the input partial point cloud. After obtaining a sparse and complete point cloud, we propose a patch-wise upsampling strategy. Patch-based upsampling allows to better recover fine details unlike decoding a whole shape, however, the existing upsampling methods are not applicable to completion task due to the data discrepancy (i.e., input sparse data here is not from ground-truth). Therefore, we propose a patch extraction approach to generate training patch pairs between the sparse and ground-truth point clouds, and an outlier removal step to suppress the noisy points from the sparse point cloud. Together with the low-res recovery, our whole method is able to achieve high-fidelity point cloud completion. Comprehensive evaluations are provided to demonstrate the effectiveness of the proposed method and its individual components.