van Rooyen, Menon, and Williamson (2015) introduced a notion of convex loss functions being robust to random classification noise and established that the “unhinged” loss function is robust in this sense. In this letter, we study the accuracy of binary classifiers obtained by minimizing the unhinged loss and observe that even for simple linearly separable data distributions, minimizing the unhinged loss may only yield a binary classifier with accuracy no better than random guessing.