A new song - A song of excellence. Give him the highest praise. See on Psalm 96:1; (note).
Hath done marvellous things - נפלאות niphlaoth, "miracles," the same word as in Psalm 96:3, where we translate it wonders.
His holy arm - His Almighty power: -
Hath gotten him the victory - לו הושיעה hoshiah llo, "hath made salvation to himself."
O sing unto the Lord a new song - Compare Psalm 33:3; Psalm 96:1. “For he hath done marvelous things.” Things suited to excite wonder, or to fill the mind with astonishment. See Psalm 77:14; Psalm 86:10.
And his holy arm - The arm of his holiness; that is, his arm put forth in a righteous cause, or vindicating that which is right.
Hath gotten him the victory - literally, “has worked salvation for him:” for himself, or in his own cause. The victory - the salvation - was really in defense of his own government; in maintaining his own authority against those who set themselves in opposition to it. What is here said may be applied to all that God does. It is really in his own cause, in order to maintain the principles of his own administration.