Beat detection systems are widely used in the music information retrieval (MIR) research field for the computation of tempo and beat time positions in audio signals. One of the most important parts of these systems is usually onset detection. There is an understandable tendency to employ the most accurate onset detector. However, there are options to increase the global tempo (GT) accuracy and also the detection accuracy of beat positions at the expense of less accurate onset detection. The aim of this study is to introduce an enhancement of a conventional beat detector. The enhancement is based on the Teager–Kaiser energy operator (TKEO), which pre-processes the input audio signal before the spectral flux calculation. The proposed approach is first evaluated in terms of the ability to estimate the GT and beat positions accuracy of given audio tracks compared to the same conventional system without the proposed enhancement. The accuracy of the GT and average beat differences (ABD) estimation is tested on the manually labelled reference database. Finally, this system is used for analysis of a string quartet music database. Results suggest that the presence of the TKEO lowers onset detection accuracy but also increases the GT and ABD estimation. The average deviation from the reference GT in the reference database is 9.99 BPM (11.28%), which improves the conventional methodology, where the average deviation is 18.19 BPM (17.74%). This study has a pilot character and provides some suggestions for improving the beat tracking system for music analysis.