no.. there is no such thing as a non allergic dog according to my son's allergist. My son has asthma and it's not the fur it's the dander which people are allergic too.
I am asthmatic, and allergic to dogs, cats an various other animals and my bichon, Paddy, does not shed fur at all! Its the best breed for this kind of thing. The only danger is when you brush out a knot, the fur will come out, so it is best to leave grooming to the groomers if you are allergic, like me!
Although there is no such thin as a hypoalergenic dog, I have pet alergies and bichons do not bother me at all. They do not shed and leave there dander everywhere
compared to petting my neighbor's golden retriever, my bichon doesnot shed, and i don't get any dander on my hands or in the air. i'm mildly allergic, and could not live in a house with a golden retireiver, but my bichon sleeps in bed with and we're just fine.