The originality of the Epistle to the Hebrews among the texts of the New Testament is a well established conviction. What this originality consists in, where it lies and how it manifests itself remain to be analysed. This article purposes to show that such a widespread and decisive notion for the Christian message as «hope» evinces particular traits in this epistle. Their presence is best understood by their relationship with Christology and, especially, with the theme of the celestial priesthood of the Son.