Yoma, Chapter Five, Mishnah Five
After having sprinkled the blood of the goat and bull inside the Holy of Holies and onto the curtain separating the Hekhal from the Holy of Holies, the priest now turns his attention to the golden altar that is inside the Hekhal.
1) And he shall go out to the altar that is before the Lord (Leviticus 16:18): that is the golden altar.
2) He then began to purify [the altar by sprinkling] in downward motion.
a) From where does he begin? From the northeast horn [of the altar], then the northwest, then the southwest, then the southeast.
b) From the place where he begins [sprinkling when offering] a sin-offering on the outer altar, there he completes [sprinkling] on the inner altar.
3) Rabbi Eliezer says: he remained in his place and sprinkled. And on every horn he would sprinkle from below upwards, with the exception of the horn at which he was standing, which he would sprinkle from above downwards.
Section one: The mishnah identifies the altar mentioned in v. 18 with the golden altar inside the Hekhal, upon which the incense is offered. This is explicit in Exodus 30:10 which in reference to this golden incense altar states, Once a year Aaron shall perform purification upon its horns with blood of the sin offering of purification; purification shall be performed upon it once a year throughout the ages. It is most holy to the Lord.
Section two: He now begins to purify the altar by sprinkling blood upon its four horns (corners), going counter-clockwise and starting at the northeast corner. The mishnah notes that he completes his sprinkling on the southeast corner, the same corner where he begins to sprinkle blood when offering a sin-offering on the outer altar. This is a sort of mnemonic used by the mishnah to remember which corner is last on Yom Kippur.
Section three: Rabbi Eliezer disagrees with the notion that he walks around the altar while sprinkling on the four horns. Rather, he remains in his spot. The whole altar was only one cubit by one cubit wide so sprinkling while standing in place would not have been difficult at all. On all of the other corners he would reach over and sprinkle with an upward motion. The exception was the corner where he was standing where for practical considerations he would sprinkle with a downwards motion.