How do I save an image without the white background?

I've designed an image in Corel Draw 10 and have not found a successful way to save it in any format that eliminates the "white box" from appearing around the image.  I have tried exporting in GIF and PNG (where at least I am given some option of transparency) but always end up with a black background upon opening after the save. 

I want to be able to give this image to another party to use ontop of their own background without the interruption of a white box surrounding it.  Hopefully, someone can walk me through a solution.