The Greek verb diatithemai (middle voice) means to arrange, dispose, or establish — particularly in the sense of making a covenant or last will and testament. In the New Testament it frequently refers to God's covenantal arrangement with humanity.
Diatithemai is the verbal form from which diatheke (covenant) derives. In Luke 22:29, Jesus uses it at the Last Supper: 'I confer on you a kingdom, just as my Father conferred one on me.' This is covenantal language — Jesus establishing the New Covenant administration. Hebrews 8-9 draws extensively on the covenant/will nuance: Christ is the mediator of a better covenant, and his death activates the 'will' (diatheke).