Automatic sleep staging provides a cheaper, faster and more accessible alternative for evaluating sleep patterns and quality compared with manual hypnogram scoring performed by a clinician. Traditionally, classification methods treat sleep stages independently of their temporal order, despite sleep patterns themselves being highly sequential. Such independent sleep stage classification can result in poor sensitivity and precision, in particular when attempting to classify the sleep stage N1, otherwise known as the transition stage of sleep which links periods of wakefulness to periods of deep sleep. To this end, we propose a novel transition sleep classification method which aims to improve classification accuracy. This is achieved by utilising both the temporal information of previous stages and treating the transitions between stages as classes in their own right. Simulations on publicly available polysomnography (PSG) data and a comprehensive performance comparison with standard classifiers demonstrate a marked improvement achieved by the proposed method in both N1 sensitivity and precision across all considered classifiers. This includes an increase in N1 precision from 0.01% to 36.75% in an MLP classifier, and an increase in both accuracy and Cohen's kappa value in two of the three classifiers. Overall best mean performance is obtained by transition classification with a random forest classifier (RF) which achieved a kappa value of κ = 0.75 (substantial agreement), and an N1 stage precision of 58%.