Final Fantasy Anniversary Edition/Labyrinth of Time

The Labyrinth of Time is the fifth secret dungeon, and a new addition to the game for the AE version.

Unlocking
The Labyrinth is only available once the Four Fiends (Lich, Marilith, Kraken, and Tiamat) are defeated. (See the main walkthrough for details.)

Once the Four are defeated, head back to Cornelia town and talk to the shadowy figure standing around the fountain. Once he runs off, follow him to the Chaos Shrine. You will see he use a secret door at the back of the Shrine; once he's gone go to the same spot and press to open the door.