Article 2 of the the United States Constitution prescribes that the President must take the oath before he enters in the execution of his Office.
The 20th Amendment; however states that the terms of the President and Vice President shall end at noon on the 20th day of January and the terms of their successors shall then begin.
It has been suggested that the wording of the 20th Amendment, that makes no reference to the oath, superseded the requirement set out in article two of the Constitution, that the oath be taken before the President begins the discharge of his duties.
It has also been suggested, however, that the oath is still necessary, because the 20th Amendment only stipulated that the four year presidential term of office shall start at noon on January 20th, not that the President shall enter upon the exercise of his Office at that moment. The start of the term does not exactly coincide with the new President entering upon the execution of his duties. President Washington's first four-year term, for instance, began on March 4th and ended exactly four years later, but he only assumed the Presidency on April 30th, when he took the oath of office. Vice-Presidents succeeding to the Presidency also assume office to finish a term that has long started. So the start of the term does not coincide with "entering upon the execution of the Office".
The controversy, however, is not of much relevance, since all Presidents who assumed office since the adoption of the 20th Amendment have continued to take the Oath. It should be noted, however, that the Presidents-elect who took office after the enactment of the 20th Amendment were not treated as President by the judges officiating at the inauguration ceremonies before the actual oath taking (e.g. Chief Justice Warren Burger asked "Vice-President" Ford, "Governor" Carter, and "Governor" Reagan if they were prepared to take the oath; Chief Justice William Rehnquist addressed George H. W. Bush and Bill Clinton as "Mr. Vice-President" and "Governor," respectively, when asking the same question; and in like manner Chief Justice Roberts posed the same question to Obama four minutes past noon, addressing him by the title of "Senator")