Brain computer interfaces (BCIs) provide a direct communication channel by using brain signals, enabling patients with motor impairments to interact with external devices. Motion intention detection is useful for intuitive movement-based BCI as movement is the fundamental mode of interaction with the environment. The aim of this paper is to investigate the temporal dynamics of brain processes using electroencephalography (EEG) to explore novel neural correlates of motion intention. We investigate the changes in temporal dependencies of the EEG by characterising the decay of autocorrelation during asynchronous voluntary finger tapping movement. The evolution of the autocorrelation function is characterised by its relaxation time, which is used as a robust marker for motion intention. We observed that there was reorganisation of temporal dependencies in EEG during motion intention. The autocorrelation decayed slower during movement intention and faster during the resting state. There was an increase in temporal dependence during movement intention. The relaxation time of the autocorrelation function showed significant (p < 0.05) discrimination between movement and resting state with the mean sensitivity of 78.37 ± 8.83%. The relaxation time provides movement related information that is complementary to the well-known event-related desynchronisation (ERD) by characterising the broad band EEG dynamics which is frequency independent in contrast to ERD. It can also detect motion intention on average 0.51s before the actual movement onset. We have thoroughly compared autocorrelation relaxation time features with ERD in four frequency bands. The relaxation time may therefore, complement the well-known features used in motion-based BCI leading to more robust and intuitive BCI solutions. The results obtained suggest that changes in autocorrelation decay may involve reorganisation of temporal dependencies of brain activity over longer duration during motion intention. This opens the possibilities of investigating further the temporal dynamics of fundamental neural processes underpinning motion intention.