Corneal Ulcers are defined as inflammation or even infection. They are one of the most frequent diseases that affect eye health. The proper measurement of corneal ulcer lesions enables the physician to evaluate the treatment effectiveness and decision making. This paper presents a segmentation method that aims to assist doctors in monitoring the treatment of corneal ulcer lesions. We applied a stepwise fine-tuning in U-Net Convolutional Neural Network architecture to train a model with 358 Point-flaky corneal ulcer images. The result from the model using U-Net architecture is then submitted to post-processing operations. Based on experiments performed with 91 Flaky corneal ulcer images, our approach achieved 0.823 of the Dice Coefficient on average, 88.9% of Recall, 99.4% of Specificity, and True Dice Coefficient of 0.835. The results are promising; we then have evidence that the proposed method could generalise the data from the training phase to segment the test data.