It is False because "In 508 BCE a limited democracy was created under the leadership of Cleisthenes.
During the Persian invasion from 480 BCE, the aristocracy took control of the city-state to organise resistance.
After the invasion was repelled, the ongoing war against Persia kept the aristocracy in control until 460 BCE when Ephialtes reestablished democratic control.
He was murdered for this, and his deputy Pericles took over and kept it going.
Pericles organised the banishment of the aristocratic leader Thucydides son of Melesias in 444 BCE, and radicalised the democracy so that the council became the servant of the popular assembly.
During the Peloponnesian War 431-404 BCE the popular assembly made crucial errors, and was replaced several times by a broadly-based oligarchy to repair the damage.
After Athens was defeated in the war in 404 BCE, there were short-term oligarchies which were eventually by a democracy."