Globally, in 2016, one out of eleven adults suffered from Diabetes Mellitus. Diabetic Foot Ulcers (DFU) are a major complication of this disease, which if not managed properly can lead to amputation. Current clinical approaches to DFU treatment rely on patient and clinician vigilance, which has significant limitations such as the high cost involved in the diagnosis, treatment and lengthy care of the DFU. We collected an extensive dataset of foot images, which contain DFU from different patients. In this paper, we have proposed the use of traditional computer vision features for detecting foot ulcers among diabetic patients, which represent a cost-effective, remote and convenient healthcare solution. Furthermore, we used Convolutional Neural Networks (CNNs) for the first time in DFU classification. We have proposed a novel convolutional neural network architecture, DFUNet, with better feature extraction to identify the feature differences between healthy skin and the DFU. Using 10-fold cross-validation, DFUNet achieved an AUC score of 0.962. This outperformed both the machine learning and deep learning classifiers we have tested. Here we present the development of a novel and highly sensitive DFUNet for objectively detecting the presence of DFUs. This novel approach has the potential to deliver a paradigm shift in diabetic foot care.