Blade of Brennaere

Blade of Brennaere is a greatsword. It inflicts fire-based damage onto targets and is thus more effective to enemies with a weakness to fire-based attacks.

Source
Blade of Brennaere can be purchased from from Culless Munitions at the Wiz Chocobo Post and Coernix Station - Cauthess for 300 gil. One can also be found in the westernmost of the Three Valleys. It can be sold back to shops for 150 gil.