In this work, we propose a special cascade network for image segmentation, which is based on the U-Net networks as building blocks and the idea of the iterative refinement. The model was mainly applied to achieve higher recognition quality for the task of finding borders of the optic disc and cup, which are relevant to the presence of glaucoma. Compared to a single U-Net and the state-of-the-art methods for the investigated tasks, the presented method outperforms others by multiple benchmarks without increasing the volume of datasets. Our experiments include comparison with the best-known methods on publicly available databases DRIONS-DB, RIM-ONE v.3, DRISHTI-GS, and evaluation on a private data set collected in collaboration with University of California San Francisco Medical School. The analysis of the architecture details is presented. It is argued that the model can be employed for a broad scope of image segmentation problems of similar nature.