The purpose of the article is to enquire into a book of the Old Testament that might throw light on some elements of continuity, discontinuity and unity between the two testaments. In order to achieve that purpose, we propose a coordination between the diachronic and synchronic methods in the exegesis of the text of Jeremiah 31, 31-34. Such a methodology would allow understanding that the New Covenant, as read by the authors of the Second Testament, does not pretend to abolish the Old one, as might be inferred from the author of the Epistle to the Hebrews. It also enables to understand that the allegorical reading of Galatians indicates more a contrast between two kinds of believers, i.e. those who come from Judaism and those from the pagan world, than a contrast between two Covenants.