This paper presents a simple argument against definitions of the death of a human being in terms of death, or the cessation of functioning, of its brain: a human being is alive, and so is capable of dying, before it acquires a brain. Although a more accurate definition is sketched, it is stressed that it should not be taken for granted that it is ethically urgent to work out such a definition. What morally matters more than the death of a human being may be something for which its death is sufficient, but not necessary, namely the irreversible loss of its capacity for consciousness. It is when we lose this capacity that we lose our moral standing, as subjects who can be benefited and harmed, and who can have rights. But, as is also suggested, the loss of this capacity is ill suited to be what the death of a human being definitionally consists of.