How to get rid of lint/fuzz on new towels?

I bought some burgundy colored towels at Kohl's and washed them before using them. When I dried off after a shower, there were red fuzz EVERYWHERE on the floor and all over me. I have washed and dried them at least 4 more times now, but still red little fuzz. Not quite as bad, but still there. What can I do to get rid of them?