We introduce a new class of sets, namely δθ-I-open sets, which form a topology finer than the topology τθ formed by the class of θ-open sets and coarser than the topology τθ-I formed by the class of θ-I-open sets. Moreover, we investigated some interesting properties of this class of sets and its relationship with the classes of the θ-open, θ-I-open and δ-I-open sets.