You have it exactly backwards. The presidential oath is the only oath required by the Constitution. The day and time of the swearing was established by legislation. The presidential oath cannot be changed except by constitutional amendment. The day and time of swearing in can be changed anytime Congress passes a new law on the matter.You are forgetting the 20th Amendment that states "The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin."Article II, Section 1, last paragraph
Before he enter on the Execution of his Office, he shall take the following Oath or Affirmation:--"I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States."
Thank you, yes. I did forget about the 20th.