Rolling element bearings are the critical parts of all rotating machinery, and their failure is one of the main reasons for machine downtime and even breakdown. The significance of early failure detection cannot be overstated, because it plays a crucial role in maintaining the proper functioning of equipment, enhancing production efficiency, and ensuring safety. Envelope analysis is the most effective and widely used failure detection approach, working according to the principle of linear filtering process of signals to remove undesirable components. However, the characteristic frequencies are often no longer evident or even overwhelmed due to the weak early failure signal. We propose an early fault feature extraction method that combines correlation entropy with an improved 2.5-dimensional square envelope spectrum. This approach is designed to overcome the relatively weak impact of early failures, which can be easily obscured by external background noise. Specifically, the correlation entropy matrix is simplified into a series of correlation entropies, and the formula for the higher-order spectrum is enhanced to achieve superior noise removal performance. Furthermore, to enhance the detection of the fault characteristic frequency (FCF), the Fourier transform in the improved 2.5-dimensional spectrum has been refined into a square envelope spectrum transform. Simulation results demonstrate that our proposed method excels at extracting early bearing fault characteristics and detecting inner and outer ring FCFs, thereby offering practical value.