  It has been shown that the theory of linear conformal quantum gravity must
include a tensor field of rank-3 and mixed symmetry [1]. In this paper, we
obtain the corresponding field equation in de Sitter space. Then, in order to
relate this field with the symmetric tensor field of rank-2, $\K_{\alpha\beta}$
related to graviton, we will define homomorphisms between them. Our main result
is that if one insists $\K_{\alpha\beta}$ to be a unitary irreducible
representation of de Sitter and conformal groups it must satisfy a filed
equation of order 6, which is obtained.
