Picori Blade
The Picori Blade is an enchanted sword that was given to the Hero of Men when the Picori appeared and was said to be one of two gifts from the Picori, the other being the Light Force. The sword was used to defeat evil and was ultimately enshrined as a sacred sword.
By the time of The Minish Cap the sword has been placed in a chest, much like how the Master Sword is placed in the Pedestal of Time, and is only brought out once a year so that the winner of the annual sword competition can have the honor of touching it. The winner of the sword competition in the year The Minish Cap takes place is Vaati.
He uses this chance to break open the chest, ultimately destroying the blade, in hopes of finding the Light Force, only to find it is not there and that he has only released demons into Hyrule which were previously captured and trapped inside by the Hero of Man.
The sword is broken by Vaati in The Minish Cap and it becomes Link's quest to reforge it. Later on, the sword is reforged by Melari and then becomes known as the White Sword. Link then takes it to the Elemental Sanctuary to infuse it with the elements he has collected. When Link first goes to the sanctuary, he has the Earth and Fire Elements. The hilt of the blade turns into the color of the latest element he collects.
Once the White Sword is infused with all of the four Elements, it becomes the Four Sword and is then used to defeat and seal Vaati away.
Trivia
The chest that seals the monsters inside it is an allusion to the Greek Myth Pandora's Box. 
The Picori Blade resembles the Master Sword because of its purple hilt. The design is also similar.
