Hypernym discovery aims to distinguish potential hypernyms for a query term. However, existing methods for hypernym discovery suffer from the following problems: (1) traditional unsupervised pattern-based methods suffer from low recall; (2) recent supervised box embedding methods are deficient in identifying specific hypernyms. To cope with the above problems, this paper presents a method for hypernym discovery based on Extended Patterns and Box Embeddings (EP-BoxE). Firstly, to acquire more hypernymy relation entity pairs, we identify co-hyponyms of a given term and use their hypernyms as the candidate hypernym set for the given term; Secondly, by analyzing the text corpus, we find that the language patterns also provide additional information for hypernym discovery, which also solves the deficiency of the box embedding methods in identifying specific hypernyms. Finally, experimentations on two domain-specific datasets reveal that EP-BoxE surpasses the performance of popular methods on the majority of evaluation metrics.