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Changes in surface electromyogram (sEMG) spectral content are commonly associated with localized muscle fatigue. However, the significance of the changes is only evident during pair-wise comparison and these can only be used for comparison between the rested and fatigued muscle and cannot be used for identifying the limit of muscle endurance without having the rested data for comparison. This is due to the large variations between sEMG at different levels of strengths of contraction, and between different people. This is further compounded when the contraction is not isometric but is cyclic because there is large variation of sEMG within each cycle. This research has developed a new sEMG based method for studying muscle fatigue and for identifying the limit of muscle endurance. It is based on motor unit synchronization and is called increase in synchronization (IIS) index. IIS index measures the level of independence between two channels of sEMG recorded from the muscle and is the log of the determinant of the global matrix ( log||G||) which is generated by performing independent component analysis on the two channels. The experimental results for biceps brachii demonstrate that when the muscle was rested, the two channels had a high degree of independence and the IIS index was greater than -0.7 (range -0.65 to -0.05). However, the channels became dependent as the muscles progressively fatigued and IIS index became less than -6.2 (range -7.8 to -6.3 ) at the limit of muscle endurance. This was irrespective of the contraction being isometric or cyclic, or of the level of muscle contraction.