If it's a vector shape, change the edge type to feather and use a high value. Once you've done that, apply a Gaussian blur.
Your eyes are capable of seeing many more colors than even the best screen driven by the best graphics card can see. The problem may be caused by the algorithm Fireworks and Illustrator are using to calculate the blur, but I believe the box you are describing is the step between the palest red your machine can draw and pure white. Note that I could not see the "bounding box" you describe until I looked at your graphic from a sharp angle rather than straight on. Anyway, the simplest solution is to spread the blur beyond the edges of the canvas. :-)
thank you, Linda
unfortunately that didn't help.
the bug is very well visible on my 27" iMac screen. the problem is I need to use the effect on a website intended for Mac community, so I can expect most of the users will also have high quality displays and will easily notice the problem as well.
spreading the blur beyond the edges of the canvas is unfortunately not an option in this case.
This occurs to me couple years ago. I remember there's a formula where you can calculate the amount of blur pixel in relate to DRES you need to set in order to get rid of the square edge and retain your effects appearance. The problem is I don’t remember what was the formula and yesterday I ran into the same problem again!
"pixel in relate to DRES you need to set" I don't understand what you mean here. What is DRES?
I found a solution in Illustrator. In the Effects Menu>Document Raster Effects Setting, there is an options section. If you type in a value in the Add: 0.0 in Around object, it will go away. I did .5 in mine. I was having the same issue as you in illustrator and this solved it.