He is to bathe himself with water in a holy place and put on his own clothes. Then he must go out and sacrifice his burnt offering and the people’s burnt offering to make atonement for himself and for the people.
Jewish Publication Society of America Version (JPS1917) - Leviticus 16:24 >And he shall bathe his flesh in water in a holy place and put on his other vestments, and come forth, and offer his burnt-offering and the burnt-offering of the people, and make atonement for himself and for the people.