AABR(automated auditory brainstem response) test is used for the screening purpose of hearing ability of neonates. In this paper, algorithm using Rolle's theorem is suggested for automatic detection of the ensemble averaged ABR waveform. The ABR waveforms were recorded from 55 normal-hearing ears of neonates at screening levels varying from 30 to 60 dBnHL. Recorded signals were analyzed by expert audiologist and by the proposed algorithm. The results showed that the proposed algorithm correctly identified latencies of the major ABR waves (III, V) with latent difference below 0.2 ms. No significant differences were found between the two methods. We also analyzed the ABR signals using derivative algorithm and compared the results with proposed algorithm. The number of detected candidate waves using the proposed algorithm was 47 % less than that of the existing one. The proposed method had lower relative errors (0.01 % error at 60dBnHL) compared to the existing one. By using proposed algorithm, clinicians can detect and label waves III and V more objectively and quantitatively than the manual detection method.