Original: The act specified that new flag designs should become official on the first July 4 (Independence Day) following admission of one or more new states. The most recent change, from 49 stars to 50, occurred in 1960 when the present design was chosen, after Hawaii gained statehood in August 1959.
Simplified: Hawaii joined on 21 August 1959 so the flag with 50 stars that is used today was not flown until 4 July 1960.