I find trainers these days are much better made than they used to be, and I never get blisters. Maybe I'm just lucky with foot shape and so on. Perhaps try different socks, or if the problem is with your heels, apply thin plasters or micropore tape to the area before setting out on your run. Failing that, the more drastic thing to do (my dad does this) is cut notches out of the achilles section of the heel tab.
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Do you lace through the top eyelet hole in the shoe? That will ften hold the shoe tight enough to make a difference.
New shoes should never give you blisters.