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F. Farshadifar introduced the notion of S -secondary submodules of an R -module M as a generalization of secondary submodules of M and provided some information about this class of submodules. Suppose that R is a Dedekind domain and M is an R -module. In this paper, we prove that if M is an S -secondary R -module withAnn R ( M ) = 0, then there exist a subsetΓofSpec ( R )and a nonzero ideal I of R such thatM ≅ ⊕ P ∈ ΓE ( R / P ) ⊕ ( ⊕i 1 ∈ Γ 1R / P 1mi 1) ⊕ … ⊕ ( ⊕i n ∈ Γ nR / P nmi n)whereP j ∈ V ( I )and{ mi j∈ N   |   i j ∈ Γ j }is a non-empty finite set( 1 ≤ j ≤ n ). So M is strongly representable. Also, we prove that if R is a domain and S is a multiplicatively closed subset of R , then R is a Dedekind domain if and only if every S -secondary R -module is strongly representable.

A new characterization of Dedekind domains