Does anybody know how to do this (I can't really explain in this title)?

I have a picture of water splashing over a black background (like this:

although this isn't the exact one). By turning the blending mode to "screen", I get the effect I want: it basically looks like the water is splashing over my image. The thing is, I need to save it as a .png file with part of the water "dripping" off the edge of my photo onto a transparent background. The problem I have is as soon as the image hits the transparent background, the black comes back.

I need a way to either remove all the black from the photo or, more ideally, find a way to make the image I see in "normal" blending mode the same as the image I see in "screen" mode. Any ideas? (I have Photoshop Elements 7.0, btw)

Thanks!