Fight on Isla de Muerta 17
"It's not a bad look, really. Eh?"
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"There are those who believe that if you hold out such a branch, it will point the way to a treasure more valuable that that ratty old cloak."
―Jack Sparrow[src]

The Branch was a branch of the tree on the Island of the Cloak of Caladonis. It was said to point to another treasure worth finding.

After unsuccessfully retrieving the Cloak of Caladonis from the serpent that guarded it, Jack grabbed a branch. He explained the significance of the branch to his crew, but much of the crew were too tired to begin another adventure.