The core-adjunct argument distinction is a basic one in the theory of argument structure. The task of distinguishing between the two has strong relations to various basic NLP tasks such as syntactic parsing, semantic role labeling and subcategorization acquisition. This paper presents a novel unsupervised algorithm for the task that uses no supervised models, utilizing instead state-of-the-art syntactic induction algorithms. This is the first work to tackle this task in a fully unsupervised scenario. .