After Ajax the Greater's death, Ajax relinquished his former "Ajax the Lesser" name.
Intending to took her as his concubine, he was stopped by fellow Argive Diomedes, outraged that Ajax had desecrated the temple of Athena. The Argives stonned him and he fled himself into the temple for sanctuary, saving him from his former brothers-in-arms, who pursued the pillaging of the city.
The violation of the temple would have effects on the dismissal of the Argive fleet. The quarrel was caused by Athena herself: While Agamemnon wished to remain to appease Athena, Menelaus pushed to leave as soon as possible as the Achaeans were eager to leave. Most of the Argives who didn't waited had easy returns, but Ajax died in a storm at the rocks called Capherides.