I don't know whether it's possible to make a frame transparent. Certainly the properties provided don't allow it.
Ali Rizwan posted an
Insight here back in 2007 showing how to turn a form transparent. If you have a look, perhaps there's something in there you can use for a frame.
Another option to consider is whether you actually need to use a frame. For instance, you may be able to simply put something like an
Image or a
Shape control on the form so that it
looks like a frame around a bunch of controls.