The 20th Amendment
The terms of the President and Vice President will start on January 20th. The terms of Congress members will start on January 3rd.
It was ratified on January 23, 1933
Before this amendment, the start of all terms was March 4th, so there was a 4-month period when the federal government couldn't effectively do anything!
This way, the new congress instead of the old congress can elect the President and Vice President if there's no majority in the Electoral College.