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Retinal images have been widely used by clinicians for early diagnosis of ocular diseases. However, the quality of retinal images is often clinically unsatisfactory due to eye lesions and imperfect imaging process. One of the most challenging quality degradation issues in retinal images is non-uniform which hinders the pathological information and further impairs the diagnosis of ophthalmologists and computer-aided analysis.To address this issue, we propose a non-uniform illumination removal network for retinal image, called NuI-Go, which consists of three Recursive Non-local Encoder-Decoder Residual Blocks (NEDRBs) for enhancing the degraded retinal images in a progressive manner. Each NEDRB contains a feature encoder module that captures the hierarchical feature representations, a non-local context module that models the context information, and a feature decoder module that recovers the details and spatial dimension. Additionally, the symmetric skip-connections between the encoder module and the decoder module provide long-range information compensation and reuse. Extensive experiments demonstrate that the proposed method can effectively remove the non-uniform illumination on retinal images while well preserving the image details and color. We further demonstrate the advantages of the proposed method for improving the accuracy of retinal vessel segmentation.