1 “O sing unto the Lord a new song”. The new man knows this, the old man knows it not. The old man is the old life, and the new man the new life: the old life is derived from Adam, the new life is formed in Christ. But in this Psalm, the whole world is enjoined to sing a new song. More openly elsewhere the words are these: “O sing unto the Lord a new song; sing unto the Lord, all the whole earth;” that they who cut themselves off from the communion of the whole earth, may understand that they cannot sing the new song, because it is sung in the whole, and not in a part of it.
Attend here also, and see that this is said. And when the whole earth is enjoined to sing a new song, it is meant, that peace sings a new song. “For He has done marvelous things.” What marvelous things? Behold, the Gospel was just now being read, and we heard the marvellous things of the Lord. The only son of his mother, who was a widow, was being carried out dead: the Lord, in compassion, made them stand still; they laid him down, and the Lord said, “Young man, I say unto you, Arise.”...“The Lord has done marvellous things.”
What marvellous things? Hear: “His own right hand, and His holy arm, has healed for Him.” What is the Lord's holy Arm? Our Lord Jesus Christ. Hear Isaiah: “Who has believed our report, and to whom is the arm of the Lord revealed?” His holy arm then, and His own right hand, is Himself. Our Lord Jesus Christ is therefore the arm of God, and the right hand of God; for this reason is it said, “has He healed for Him.” It is not said only, “His right hand has healed the world,” but “has healed for Him.”
For many are healed for themselves, not for Him. Behold how many long for that bodily health, and receive it from Him: they are healed by Him, but not for Him. How are they healed by Him, and not for Him? When they have received health, they become wanton: they who when sick were chaste, when cured become adulterers: they who when in illness injured no man, on the recovery of their strength attack and crush the innocent: they are healed, but not unto Him. Who is he who is healed unto Him?
He who is healed inwardly. Who is he that is healed inwardly? He who trusts in Him, that when he shall have been healed inwardly, reformed into a new man, afterwards this mortal flesh too, which does languish for a time, may in the end itself even recover its most perfect health. Let us therefore be healed for Him. But that we may be healed for Him, let us believe in His right hand.
Source: The Enarrations, or Expositions, on the Psalms (New Advent)