One of the main objectives of Palaeolithic art researchers is to study and systematise the form of artistic representations. Some methodologies include the analysis of qualitative variables, linear measurements or the use of geometric morphometry with landmarks. However, these techniques depend to a large extent on the subjectivity of the researcher, which often leads to biased results. To overcome this issue, we present an application of geometric morphometry using Elliptic Fourier Analysis (EFA), together with multivariate statistics and hypothesis testing, for the first time to the study of form in prehistoric art. In order to explain its use, the “duck-bill” convention of pre-Magdalenian horses, often used as a chronological and geographical marker, has been used as a case study. This formalism is described disparately in the literature, so the main objective is to use EFA to determine whether it is possible to characterise this type of convention according to the definitions given by certain authors. The results indicate a possible classification of the heads of these animals. Through this taxonomic proposal, it has been possible to verify the great diversity of forms in which the authors classify the duck-bill horses and, therefore, to demonstrate that this peculiar form can be considered neither a conventionalism nor a chronological/regional marker. In conclusion, the methodology based on EFA combined with multivariate statistics for the objective study of form in prehistoric art is effective and opens a new avenue of analysis in the art of prehistoric societies.