Evaluation of synchronization between signals can give new insights into the functioning of the related systems. Methods that can detect synchronization or coupling between signals can be divided two types: linear and non linear methods. In this paper we use the non linear correlation coefficient (h2) to show the difference in synchronization between efficient uterine contractions during labor and normal physiological contractions during pregnancy, in uterine activity bursts recorded at different places on the pregnant abdomen. Our interest in the non linear correlation coefficient is based on the fact that the propagation mechanism of uterine EMG signal may be strongly non linear. The results obtained from estimating the synchronization between 16 uterine EMG channels indicate that synchronization between contractions as measured by h2 is stronger in labor than in pregnancy. Limited data indicates that the h2 value increases markedly with term when expressed in duration before spontaneous labor.