Scarf shedding fibres

[ridinghighinapril]

I wasn't sure if this was strictly S&B but couldn't figure out where in Home & Garden to put it....

....I have a lovely warm scarf that sheds fibres over my clothes and seriously restricting what I can wear it with. I have washed it on wool program but it doesn't seem to have made a difference.
Any pointers to minimising this? TIA