Deep Matching (DM) is a popular high-quality method for quasi-dense image matching. Despite its name, however, the original DM formulation does not yield a deep neural network that can be trained end-to-end via backpropagation. In this paper, we remove this limitation by rewriting the complete DM algorithm as a convolutional neural network. This results in a novel deep architecture for image matching that involves a number of new layer types and that, similar to recent networks for image segmentation, has a U-topology. We demonstrate the utility of the approach by improving the performance of DM by learning it end-to-end on an image matching task.