  We prove an automorphic analogue of Deligne's conjecture for symmetric fourth
$L$-functions of Hilbert modular forms. We extend the result of Morimoto based
on generalization and refinement of the results of Grobner and Lin to
cohomological irreducible essentially conjugate self-dual cuspidal automorphic
representations of ${\rm GL}_2$ and ${\rm GL}_3$ over CM-fields.
