Let {A, B} be a complete system of the closed orientable surface F of genus 2. A simple closed curve C on F is separating with respect to (A, B) if it is disjoint from A ∪B and it cuts F into two once-punctured tori X, Y with A () X, B () Y. Let γ be a simple closed curve on F which is disjoint from A ∪ B and intersects C essentially in two points. In this paper, we show that up to isotopy,{hnγ(C): n ∈ Z} is the set containing all the simple closed curves on F which is separating with respect to (A, B), where hγ is the Dehn twist along γ on F. This also shows how two simple closed curves on F which are separating with respect to (A, B) are related. The result can be applied to yield all Haken spheres of a Heegaard splitting V∪F W which are weakly equivalent to a given Heken sphere of the splitting.