The interpretation of the Old Testament in Hebrews, so fundamental to the letter’s argument, is a subject addressed by all commentators, and it has been the specific focus of numerous very valuable studies over the years (such as those by, for instance, Markus Barth, George Caird, and Graham Hughes). This paper will argue, however, that the application to Hebrews of a new methodology may enable us to better understand the author’s use of the Old Testament and to identify some of his characteristic exegetical techniques which have been previously overlooked. The approach advocated here begins from the premise that Hebrews should be placed firmly within the context of early Jewish bible interpretation, and is inspired by current research within the field of Jewish Studies, particularly the work of Alexander Samely, who has within the last decade developed a highly sophisticated methodology for defining targumic and mishnaic exegetical techniques. Some key sections of the letter which draw heavily on scripture will therefore be analysed to illustrate this methodology, including Heb 7:1-10 (Melchizedek) and Heb 11:1-22 (the patriarchs in the Book of Genesis. The paper will use these passages to seek to explore issues such as: the relationship between Hebrews and other genres of scriptural interpretation found within early post-biblical Judaism, including targum and rewritten bible; the attitude taken to reproducing the exact wording of a scriptural text; the techniques by which a text could be assigned as relevant to a particular topic; the ways in which the author prepares his audience for his ensuing interpretation of scripture by the provision of new literary context for a citation; and the factors which allowed for the linking of two or more scriptural texts.