  Let X be a K3 surface with a polarization H with H^2=2rs. Assume that
H.N(X)=Z for the Picard lattice N(X). The moduli space Y of sheaves over X with
the Mukai vector (r,H,s) is again a K3 surface.
  We prove that Y\cong X, if there exists h_1\in N(X) with (h_1)^2=f(r,s),
H.h_1\equiv 0\mod g(r,s), and h_1 satisfies some condition of primitivity.
Existence of such type a criterion is surprising, and also gives some geometric
interpretation of elements in N(X) with negative square.
  We describe all 18-dimensional irreducible components of moduli of the (X,H)
with Y\cong X and prove that their number is infinite.
  These generalizes results of math.AG/0206158, math.AG/0304415 for r=s.
