EEG (electroencephalogram) is generated by the brain activity and is present in the central nervous system of spontaneous electrical activity, which is an important biological signal. EEG is a very weak and nonlinear as well as irreversible signal. This paper presents a new method to describe it based on the relative entropy of transition probability for the forward and reverse sequences. Besides, we may apply this method to study the normal EEG and epileptic EEG irreversibility, and the experimental results show that the EEG irreversibility of patients who suffer from epilepsy is significantly less than that of normal people. This shows that the relative transfer entropy can be used as aparameter to detect the irreversible degree of EEG for recognizing whether a patient is suffering from epilepsy or not, which may be a positive index for clinical diagnosis.