Let (X, τ, I) be an ideal topological space. For a subset A of X, a local function Γ*(A)(I, τ ) is defined as follows: Γ *(A)(I, τ ) = {x in X : A ∩ U not in I, for every regular open set U containing x}. This coincides with the δ-local functions due to Hatir et al. [2]. By using Γ* (A)(I, τ ), an operator Ψ_Γ* : P(X) → τ ^δ is defined as the dual of the δ-local func-tion and its relations with δ-codense ideals are investigated.