Gosh, an image would have been so instructive. Since you forgot to post it, I can only imagine. Basically to turn the outermost black boundary white, I'd invert the image (so now it's white that touches the edge of the image, not black), then get rid of white blobs touching the edge of the image, then invert again to make your black band black again.
binaryImage = ~imclearborder(~binaryImage);
If that doesn't work, then attach your image.