Some people who wish to become a living donor are not compatible with the intended recipient. For instance, a donor may have blood type A, while the recipient blood type B. Depending on your incompatibility, other approaches to transplant are available.
A donor exchanges his or her kidney with a living donor from another incompatible donor/recipient pair to create two compatible pairs.
The donor will not directly donate his or her kidney to the intended recipient, but exchanging with another incompatible pair will allow for two compatible transplants.