To start, you will need to cut into your fabric from the selvage edge. Spread the fabric and a thread should show itself. Then, gently pull the thread as shown in the image below.
Continue to gently pull the thread, the entire way across your fabric, until you get to the other selvage edge. Your thread may break and that is OK. Just pick out another thread and continue across.
Once you have pulled out your thread, you will see that there is a definite line. This is your cutting line. It is perfectly straight.
Now you can cut your perfectly straight strip of fabric. This works well for waistbands and bindings that are cut on the straight of grain. It is also a nice way to straighten up the cut end of your fabric lengths.