Inter-hemispheric asynchrony within the multichannel recordings of newborn EEG is associated with abnormal functionality of the newborn brain. Mean Phase Coherence (MPC) as a bivariate phase synchrony measure is widely used for pair-wise comparisons of scalp EEG phase information. A bivariate measure, however, is unlikely to capture the key feature of asynchrony seen in the sick neonatal brain, which is characterized by a global disruption of synchrony. In this study, the concept of cointegration is employed to generalize the bivariate MPC to deal with the multivariate case. The performance of the generalized MPC (GMPC) is evaluated using two simulated signals. It is also tested on a multichannel newborn EEG dataset with asynchronous inter-hemispheric bursts. The proposed method can be used to detect and quantify the degree of inter-hemispheric asynchrony from EEG signals.