Yes. Under the Flag Act of 1818, it was decreed that new stars would be added on the July 4 following the state's formal admission. So, Alaska's star was added on July 4, 1959, and Hawaii's star was added on July 4, 1960.

For more information on the design of the 49-star and 50-star flags, the U.S. Army's Quartermaster Corps details that process in a 1959 issue of Army Information Digest.