Making an object a single solid colour?

[JonnyT]

I've got this image of a black sword outline on a white background. I want to remove the white background so that just the black outline of the sword is left behind. But when I do that there's a halo of white around the sword left behind from the original white background:



Is there a way to take the Sword and make every pixel in that layer black?

Or is there a better way of achieving this result?

I've been searching for ages but it's hard to find the answer to your question when you don't know the right terminology to search for.