Something about how I place my hands on the bars causes it to creep in opposite directions and I end up with a patch of bare bar. Not good for the hands. So, I took the tape off and re-wrapped from the brake up - tight - and then taped the end with electrical tape. No more problems, and it was easy (even for a person who is mechanically chanllenged ). It took less than 10 minutes.

If the tape itself is split, replace it...