Joining of ends on binding is my specialty. I've demo-ed it several times.
*First join all binding strips, and lay the binding on the quilt so that you don't get seams too close to a corner.
*Press a triangle into the beginning. When it's on the quilt, turn down the top edge so that it is even with the raw edge on the side. Crease this well or draw a line on that crease so you can see it.
*Start sewing on the binding about 8 to 10 inches from this triangle. Leave that tail free.
*Now go back and put a pin in the quilt about 16 to 20 inches from where you started sewing. This is where you will stop at the end. (I'm not going to go through how to do the mitered corners here.)
*Sew around to the pin. Take the quilt out of the machine.
*Pin binding as you will want it to lay. Snug it up a little. Now ends of binding are overlapping.
*Cut off the end of the binding at the bottom of the triangle. The two pieces will be overlapping exactly as long as the binding is wide. It doesn't matter how wide your binding is. The triangle will be the correct measurement.
*Take the pins out. Pick up both ends RST. Find where the crease of the triangle is and twist these two pieces so that the crease is going side to side, not top to bottom. Pin very well.
*Sew on the crease.
*Snap the quilt straight and see if the binding fits now. If you sewed top to bottom, it won't work. Frog stitch and do it again. Sometimes that happens.
*Finger press the seam open. Then trim out the seam allowance.
*Carefully fold the binding in half with the seam allowance still open.
*Sew this last piece of binding onto the quilt.
It will be very hard to see where your binding was sewn together. That seam looks exactly like any other seam in your binding.
Hope this works for you.