In our Orthodox Church the Mystery of Unction of Sick is only administered to Orthodox believers who are in full communion as the case in all other Mysteries (of course, except for Baptism).

The person to receive the Mystery should be a baptized believer, to repent, and fast if he is able. However, a priest can pray on a sick unbeliever and anoint him with what we call simple oil (used in Baptism or blessed oil as people receive from a monastery, but not the oil of the Mystery of Anointing of Sick.

- Bishop Serapion