Electroencephalography (EEG) is an important clinical tool for reviewing sleep-wake cycling in neonates in intensive care. Trace alternant (TA)-a characteristic pattern of EEG activity during quiet sleep in term neonates-is defined by alternating periods of short-duration, high-voltage activity (bursts) separated by lower-voltage activity (inter-bursts). This study presents a novel approach for detecting TA activity by first detecting the inter-bursts and then processing the temporal map of the bursts and inter-bursts. EEG recordings from 72 healthy term neonates were used to develop and evaluate performance of 1) an inter-burst detection method which is then used for 2) detection of TA activity. First, multiple amplitude and spectral features were combined using a support vector machine (SVM) to classify bursts from inter-bursts within TA activity, resulting in a median area under the operating characteristic curve (AUC) of 0.95 (95% confidence interval, CI: 0.93 to 0.98). Second, post-processing of the continuous SVM output, the confidence score, was used to produce a TA envelope. This envelope was used to detect TA activity within the continuous EEG with a median AUC of 0.84 (95% CI: 0.80 to 0.88). These results validate how an inter-burst detection approach combined with post processing can be used to classify TA activity. Detecting the presence or absence of TA will help quantify disruption of the clinically important sleep-wake cycle.