Data-driven approaches have been proved effective for remaining useful life estimation of key components (bearings for example) in rotating machinery. In such approaches, it is important to determine an appropriate degradation indicator from the collected run-to-failure life cycle data. In this paper, a new degradation indicator is introduced based on the joint approximate diagonalization of eigen matrices algorithm. First, a matrix consisting of time domain, frequency domain, and time–frequency domain features extracted from the collected data instances is created. Then a two-layer joint approximate diagonalization of eigen matrices is introduced to transform the matrix to the advanced features (a vector) that represents the behavior of the bearing’s degradation. As an independent component analysis method, the designed two-layer joint approximate diagonalization of eigen matrices is able to eliminate the redundancy of the directly extracted features. Further, the obtained vector is input into an extreme learning machine to train a remaining useful life prediction model. Finally, a set of experimental cases are utilized to verify the presented method. Results show that the two-layer joint approximate diagonalization of eigen matrices is capable of exploring features that reflects the trend of bearing’s degradation state much better. And due to the easy parameter configuration and fast learning speed, the extreme learning machine is capable of training a model that can effectively predict the remaining useful life of the bearings.