  Two birational subvarieties of P^n are called Cremona equivalent if there is
a Cremona modification of P^n mapping one to the other. If the codimension of
the varieties is at least 2 then they are always Cremona Equivalent. For
divisors the question is much more subtle and a general answer is unknown. In
this paper I study the case of rational quartic surfaces and prove that they
are all Cremona equivalent to a plane.
