The analysis of broken glass is forensically important to reconstruct the events of a criminal act. In particular, the comparison between the glass fragments found on a suspect (recovered cases) and those collected on the crime scene (control cases) may help the police to correctly identify the offender(s). The forensic issue can be framed as a one-class classification problem. One-class classification is a recently emerging and special classification task, where only one class is fully known (the so-called target class), while information on the others is completely missing. We propose to consider classic Gini's transvariation probability as a measure of typicality, i.e. a measure of resemblance between an observation and a set of well-known objects (the control cases). The aim of the proposed Transvariation-based One-Class Classifier (TOCC) is to identify the best boundary around the target class, that is, to recognise as many target objects as possible while rejecting all those deviating from this class.