This study proposes a new method for detecting and diagnosing fault information for rolling bearings. First, a novel method called complete ensemble intrinsic timescale decomposition with adaptive noise is proposed. Compared with the complete ensemble empirical modes decomposition with adaptive noise (CEEMDAN) method, the proposed method reduces the spurious mode, which interferes with the identification of feature frequency in rolling bearings. In addition, when a typical mode mixing signal is decomposed, the mode mixing problem that appears in the adjacent mode components of the CEEMDAN method is also solved. Second, there is only an intrinsic mode function, which mostly reflects the vibration feature of a rolling bearing. We propose a new method to evaluate these mode functions to determine which mode function contains the most useful information. Our proposed method solves the problem using traditional time-domain analysis methods of a single dimensionless parameter with poor stability and low sensitivity. Our method includes sample entropy, kurtosis, the zero-crossing rate, and a correlation coefficient. The proposed method reduces the limitations of each method to select the sensitive component. Finally, we use a simulation signal and an experimental signal to verify the effectiveness of the proposed method.