Disclaimer: I have not read any of the Harry Potter books.
In the movie, Harry Potter and the Sorcerer's Stone, during the scene when the centaur is explaining the nature of drinking unicorn blood to Harry, the movie pans across the dead unicorn. One can see the unicorn's horn and, laying beyond the horn and head, a sword.
Is there significance to the sword in the story/canon, or is it merely a prop, the means of killing the unicorn?