A two-phase novelty detection approach to locating abnormalities in the descent phase of aircraft flight data is presented. It has the ability to model normal time series data by analyzing snapshots at chosen heights in the descent, weight individual abnormalities, and quantitatively assess the overall level of abnormality of a flight during the descent to a given runway. The method models normal approaches to a given runway (as determined by the airline's standard operating procedures) and detects and ranks deviations from that model. The approach expands on a recommendation by the UK Air Accident Investigation Branch to the UK Civil Aviation Authority. The first phase quantifies abnormalities at certain heights in a flight. The second phase ranks all flights to identify the most abnormal, each phase using a one-class classifier. For both the first and second phases, i.e., the support vector machine (SVM), the mixture of Gaussians and the K-means one-class classifiers are compared. The method is tested using a data set containing manually labeled abnormal flights. The results show that the SVM provides the best detection rates and that the approach identifies unseen abnormalities with a high rate of accuracy. The feature selection tool F-score is used to identify differences between the abnormal and normal data sets. It identifies the heights where the discrimination between the two sets is largest and the aircraft parameters most responsible for these variations. The method presented adds much value to the existing event-based approach.