In this paper we describe learning of a descriptor based on the Siamese Convolutional Neural Network (CNN) architecture and evaluate our results on a standard patch comparison dataset. The descriptor learning architecture is composed of an input module, a Siamese CNN descriptor module and a cost computation module that is based on the L2 Norm. The cost function we use pulls the descriptors of matching patches close to each other in feature space while pushing the descriptors for non-matching pairs away from each other. Compared to related work, we optimize the training parameters by combining a moving average strategy for gradients and Nesterov's Accelerated Gradient. Experiments show that our learned descriptor reaches a good performance and achieves state-of-art results in terms of the false positive rate at a 95% recall rate on standard benchmark datasets.