Maya Modeling :: How To Make A Symmetrical Texture Map For Character

I am currently trying to make a symmetrical texture map for my character.

For example, I want the arms of a character to share the same texture pattern.

But I can't place the UV shell corresponding to one arm on top of the piece corresponding to the other arm because it doesn't match without flip.

If I'm trying to flip this shell it becomes shaded with a semi-transparent red color. But all UV shells must be shaded with blue and have a clockwise winding order. Am I right ?

Is there a way to reverse the winding order so the UVs match the original half's without physically flipping the UV shell on the U or V.