Modern machine degradation trend evaluation relies on the unsupervised model-based estimation of a health index (HI) from asset measurement data. This minimizes the need for timely human evaluation and avoids assumptions on the degradation shape. However, the comparability of multiple HI curves over time generated by unsupervised methods suffers from a scaling mismatch (non-coherent HIs) caused by the slightly different asset initial conditions and distinct HI model training. In this paper, we propose a novel self-supervised approach to obtain HI curves without suffering from the scale mismatch. Our approach uses an unsupervised autoencoder based on a convolutional neural network (CNN) to detect initial faults and autonomously label measurement samples. The resulting self-labeled data is used to train a 1D-CNN health predictor, effectively eliminating the scaling mismatch problem. On the basis of a bearing test-to-failure experiment, we show that our self-supervised scheme offers a promising solution for the non-coherent HI problem. In addition, we observed that our method indicates the gradual wear affecting the bearing prior to the independent analysis of a human expert.