Learning a feature point detector presents a challenge both due to the ambiguity of the definition of a keypoint and correspondingly the need for a specially prepared ground truth labels for such points. In our work, we address both of these issues by utilizing a combination of a hand-crafted Shi detector and a neural network. We build on the principled and localized keypoints provided by the Shi detector and perform their selection using the keypoint stability score regressed by the neural network - Neural Stability Score (NeSS). Therefore, our method is named Shi-NeSS since it combines the Shi detector and the properties of the keypoint stability score, and it only requires for training sets of images without dataset pre-labeling or the need for reconstructed correspondence labels. We evaluate Shi-NeSS on HPatches, ScanNet, MegaDepth and IMC-PT, demonstrating state-of-the-art performance and good generalization on downstream tasks.