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Focusing on the complicated pathological features, such as blurred boundaries, severe scale differences between symptoms, background noise interference, etc., in the task of retinal edema lesions joint segmentation from OCT images and enabling the segmentation results more reliable. In this paper, we propose a novel reliable multi-scale wavelet-enhanced transformer network, which can provide accurate segmentation results with reliability assessment. Specifically, aiming at improving the model's ability to learn the complex pathological features of retinal edema lesions in OCT images, we develop a novel segmentation backbone that integrates a wavelet-enhanced feature extractor network and a multi-scale transformer module of our newly designed. Meanwhile, to make the segmentation results more reliable, a novel uncertainty segmentation head based on the subjective logical evidential theory is introduced to generate the final segmentation results with a corresponding overall uncertainty evaluation score map. We conduct comprehensive experiments on the public database of AI-Challenge 2018 for retinal edema lesions segmentation, and the results show that our proposed method achieves better segmentation accuracy with a high degree of reliability as compared to other state-of-the-art segmentation approaches. The code will be released on: https://github.com/LooKing9218/ReliableRESeg.