Currently, computational tools and analyses play an essential role in medical diagnosis including epilepsy. One of the most important applications in epilepsy is epileptic seizure classification and detection. In this study, the characteristics of spectral exponent γ obtained from the wavelet-based approach are examined. From the computational results, it is evidenced that the higher and lower frequency components of intracranial EEG data exhibit remarkably different spectral exponent characteristics. Furthermore, the difference between spectral exponents obtained from higher and lower spectral subbands, referred to as the spectral exponent difference, of intracranial EEG data recorded during non-seizure period and during epileptic seizure activity is intriguing and thus can be used as an excellent feature for epileptic EEG data classification. The performance evaluation demonstrates that the spectral exponent difference is the best single feature for epileptic EEG data classification. The mean sensitivity and the mean specificity of the epileptic EEG data classification using the feature of spectral exponent difference are, respectively, 99.01% and 92.40%.