Skylark: if you fold your fabric so that the selvedges are exactly straight, you can fold to four or eight layers. Clip these edges together. I would pin that with flat head pins in the area you will not be cutting. Take off the clips. Then put your ruler on the width of the strip you want PLUS what you want to cut off of the selvedge. Be sure you ruler is completely perpendicular to the folds. That would make a very straight strip. Without moving the fabric (turn the cutting board), Cut the width of the strip from the selvedge, lining up the ruler on the fold again.
Hope this works for you.