This sacrament is unique in that the minister is not a deacon, or a priest, or a bishop, or even the Pope! The priest or deacon who officiates is only a witness. In Matrimony, man and woman are both the subjects (the ones who receive) and the ministers (the ones who carry out or execute) of the sacrament.
“The sacrament of Matrimony establishes a perpetual and exclusive bond between the spouses. God himself seals the consent of the spouses. Therefore, a marriage which is ratified and consummated between baptized persons can never be dissolved” (CCCC 346).