[Jemma]

Only the VERY experienced breeders should even attempt this. And this means knowing every dog in both pedigrees and knowing they all have cleared any problems that afflict that breed. To say it can backfire on a breeder is a understatement. It takes so much research on the bloodlines of the dogs you are considering. Remember, you can double up on recessive genes and end up with a litter with major problems.
You don't need to do inbreeding to keep a Yorkie bloodline. You can do a lot of research on a male AKC dog to breed with a non relative female and keep the Yorkie bloodline. You want to better the breed. Example, if you have a female with a slight fault you want to look for a male that doesn't have the fault but rather closest to the standard. If you breed to a male with the same fault what kind of pups will turn out. Most with the same fault as the parents.