'Order of Melchizedek' in the Bible

And He says in another place [Psa. 110:4], "You are a priest forever according to the order of Melchizedek." [Note: This is the first mention of this mysterious Old Testament priest who, throughout this book, is represented as a type of Christ].

[So], God declared Him to be a Head Priest according to the order of Melchizedek.

where Jesus, our forerunner, [already] entered on our behalf, having become a Head Priest forever according to the order of Melchizedek.

So, if perfection [i.e., a right relationship with God] could have been attained through the Levitical priesthood, (for under it people had received the law of Moses), what further need would there have been for another priest to arise, according to the order of Melchizedek, who was not considered "according to the order of Aaron"?

For it is declared [about Jesus in the Scriptures, Psa. 110:4], "You are a priest forever according to the order of Melchizedek."