When it first became independent, in 1962, it had a sorghum plant and a drum in the middle instead of the stars:

When the monarchy was abolished in 1966, the drum was removed, as it was a royal symbol:

In 1967, they finally settled on the three stars in the middle, representing the three ethnic groups of Burundi: Hutu, Tutsi and Twa.

They actually changed the aspect ratio in 1982, so the title is not entirely correct, but today still seems like the most appropriate day to post their flag.