Need 1px thick border with rounded corners, inside transparent

I'm looking for a super smooth rectangular (but rounded corners) border that is transparent on the inside, white on the outside.

The best I could do in illustrator and photoshop still has a bit of "white" on the inside edge.

can someone give me a walkthrough of how to make a really thin (1pixel) border? It needs to be put onto a website.

It has to be super smooth. I've seen them kinda pixelated, but I"ve gotten it really smooth in AI and PS. I just need the inside to be totally transparent.

Thanks!!

Why don't you upload an example? I can't imagine what you are trying to do with 1px

like a border. you know on websites if you want a border, you can set it to 1px wide. I just want one that has a round corner.

You can draw circles in PAINT then crop the corners. I suppose you intend to build a table and place the four rounds on the corners?
You'll get softer edges if you can settle for a color other than black. That way you can open it in an image editor and either soften and blur the pixels. I've seen too many issues with .png files so, you will have to find a way to add transparency to the inside. Try gifworks.com (http://www.gifworks.com/) if you don't have any other program. PAINT will take the transparency off if you try to edit.