It is usually not recommended to limit your donor search by trying to match a donor’s blood type to your own. But for some intended parents, especially those of certain cultures or religions, blood type is an important factor for personal reasons. Medically speaking, blood type is not important in third party reproduction.

The four basic blood types are O, A, B, and AB. O is the most common type, and AB is the least common. We all inherit one allele from each of our parents. The three basic blood type alleles are A, B, and O. Possible allele combinations are:
                                                OO
                                                AO
                                                BO
                                                AB
                                                AA
                                                BB

Blood types A and B are codominant alleles; blood type O is a recessive allele. A codominant allele is apparent even if only one is present; a recessive allele is apparent only if two recessive alleles are present. Therefore, since blood type O is recessive, it is not apparent if the person inherits an A or B allele along with it.

Possible allele combinations result in a particular blood type, as follows:

                                               OO = blood type O
                                               AO = blood type A
                                               BO = blood type B
                                               AB = blood type AB
                                               AA = blood type A
                                               BB = blood type B

You can see that a person with blood type B may have a B and an O allele, or that person may have two B alleles. If both parents are blood type B and both have a B and a recessive O, then their children will be either BB (if each parent passed on the B allele), BO (if one parent passed on B and the other parent passed on O), or OO (if both parents passed on the O allele). If the child is BB or BO, he or she has blood type B. If the child is OO, he or she has blood type O.

Therefore, you can see that it is not at all unusual for two parents with blood type B (or blood type A) to have children with blood type O.