In this paper, we have developed a new measure of understanding the temporal evolution of phase synchronization for EEG signals using cross-electrode information. From this measure it is found that there exists a small number of well-defined phase-synchronized states, each of which is stable for few milliseconds during the execution of a face perception task. We termed these quasi-stable states as synchrostates. We used k-means clustering algorithms to estimate the optimal number of synchrostates from 100 trials of EEG signals over 128 channels. Our results show that these synchrostates exist consistently in all the different trials. It is also found that from the onset of the stimulus, switching between these synchrostates results in well-behaved temporal sequence with repeatability which may be indicative of the dynamics of the cognitive process underlying that task. Therefore these synchrostates and their temporal switching sequences may be used as a new measure of the stability of phase synchrony and information exchange between different regions of a human brain.