DISCLAIMER: This is NOT my own method. I learned this from watching Simply Quilts on HGTV a while back. I am simply sharing what I learned with you.
Here is a simple way to end your binding with a diagonal seam rather than a straight seam.
First of all, you want to make sure you have enough binding so that it can overlap about 8-12 inches on both ends.
Secondly when you start your binding, make sure this end is cut at a 45 degree angle and leave 8-12 inches free at the beginning like this:
Stitch your binding down in whatever manner you usually use, mitering corners, etc.
If you need a great binding tutorial check out my friend Amanda's blog, she has a great tutorial for calculating the length of the strips, mitering corners and finishing your binding.
When you get back around to the beginning, stop stitching about 8-12 inches from where the beginning edge of the binding would be if you laid it along the edge of the quilt.
When both ends are laid along the edge of the quilt there should be several inches of overlap. There should be about 8-12 inches of overlap. If you have a lot of excess binding it would be a good idea to trim it off now. Trim it from the end where you ended your stitching, not from the beginning where you have your 45 degree angle.
Make sure the quilt is flat and your binding is placed just as if you were going to sew it, nice and flat and placed in the correct place. Place the ending end inside the beginning end like this.
Once they are placed together like this, then make a small mark on the ending end of the binding at the points of the 45 degree angle from the beginning end.
Take the ending end and open out the fold. Matching up the two marks as best as possible, draw a line at 45 degrees.
Then, using your ruler, draw another line parallel to the first line one half inch away toward the free end of the binding strip.
Cut on this line.
Now make a small mark one quarter inch from each edge.
Using the quarter inch marks as a guide, place the ends of the binding right sides together at a right angle with the diagonal edges flush. There should be little triangles sticking out on either end.
Stitch this together on your machine using a quarter inch seam allowance.
Finger press the inside seam allowance to one side or the other. It doesn't make any difference which direction you go. Re-fold the binding back in half lengthwise. If you have been careful, then it should lay perfectly along the edge of your quilt and the creases from the original lengthwise fold should match up. You can clip off the little triangles that stick out from the binding if you want to at this point.
Pin your binding to the edge of the quilt and sew it down. Make sure to backstitch a couple of stitches at the beginning and end so that your binding stays in place.
That's all there is to it!
Feel free to ask me if yo have any questions or if there is something that is unclear.