This paper proposes a modified U-Net neural network architecture to segment the optic disc from retinal fundus images because it allows for early detection and treatment of glaucoma, a serious eye disease. Since manual segmentation is time-consuming and influenced by operator experience, automated methods have been developed, including image processing and deep learning algorithms. The proposed technique is based on the use of a modified U-net CNN applied on the PAPILA dataset, which includes 244 patient records, achieving an Intersection over Union (IOU) of 91% on the validation set for the optic disc class. Compared to other state-of-art works, this method outperforms them even if it is applied to a smaller dataset, demonstrating its potential for use in clinical practice. Indeed, the proposed method could improve the diagnosis and monitoring of eye diseases and provides valuable assistance to medical professionals.