  Let n be any integer greater than two. We prove that there exists a
projection P having the following properties. (1) P is not the projection of
any unknotted knot. (2) The singular point set of P consists of double points.
(3) P is the projection of an n-knot which is diffeomorphic to the standard
sphere.
  We prove there exists an immersed n-sphere (in R^{n+1}\times{0}) which is not
the projection of any n-knot (n>2). Note that the second theorem is different
from the first one.
