Sprite and transparency

I got a sprite with a white background but I would like the background transparent …
How do I get there? It looks like this:
https://www.dropbox.com/s/xecifjm9n2t9ctj/Foto%2028.06.13%2019%2034%2015.png

You could replace all the white pixel values with color(0,0,0,0). But the border will not be nice.

Thx.
Setting the background to rgb(256,256,256) didnt work, but I found and erase tool (erase pixel data). That did the trick.