The match of donor and recipient histological (HLA) compatibility systems is essential for successful stem cell transplantation. For a newborn, one’s umbilical cord blood is perfectly compatible. The probability of compatibility in siblings is very high at 1:4, meaning that the blood of the stored umbilical cord in 25% of cases is fully compatible with the sibling. The probability of biological compatibility of non-related individuals is very low, at 1:70000. It should be noted that the development of transplant technologies made it possible to carry out haplo-identical (i.e., 50% compatible) transplants. Thus, a parent and a semi-compatible sibling can use blood. Similarly, these technologies will make it easier to transplant even if there is a non-compatible (less than 50%) donor and recipient. Therefore, in some cases, it will be possible to use UCB for a wider circle of recipients, primarily for family members and relatives.