Yes, one of the many unpleasant side effects of Prednisone. I'm at 10mg now and I don't bleed so bad anymore but just a little scratch will cause the skin tissue from the wound outward to turn a nasty red and it takes a week or two to go away. It usually happens on my arms so I'm glad it is now long sleeve shirt weather. As the others said - hang in there - it will get better.