>>1-kun, there are two major schools of thought about that self-referential process.
The first school says that since the deathnote is killing itself, the process cannot complete, and so the true extent of the deathnote cannot be fulfilled.
The second school says that any sufficiently advanced system of deathnoting has subcomponents that must worth together to actuate a complete deathnoting, and when you start to kill the combined system, it fails part of the way through, yet the failure still succeeds in killing the deathnote.