The relation of the gift may be defined by the threefold obligation set out by M. Mauss: to give, to receive, and to reciprocate. In the domain of organ transplantation, a materialist conception of this obligation runs into a dead end: the recipient is unable to give back the organ received from the donor. Our analysis offers a conception of the debt as a new gift that can very easily be given in a different way, to somebody else. To this, we add the clinical observation that patients construct a myth of the gift, by virtue of which they manage to form for themselves an imaginary representation of the donor.