Thin line between pattern tiles in Illustrator CS

I've been making borders by making a square swatch and then using it
to make a pattern brush. Then I make a rectangle and choose the
pattern brush I just made for the stroke. However, when the graphic
displays, there are often very thin, faint lines between tiles. They
don't appear between every tile, but usually between every 2 tiles.
The problem is only on screen--the graphics print fine. Does anybody
know why these faint lines are appearing, and if there is anything I
can do about them? Thanks!