Let B be a unital C * -algebra and H a finite dimensional C * -Hopf algebra with its dual C * -Hopf algebra H 0 . We suppose that there is a saturated action of H on B and we denote by A its fixed point C * -subalgebra of B. Let E be the canonical conditional expectation from B onto A. In the present paper, we shall give a necessary and sufficient condition that there are a weak action of H 0 on A and a unitary cocycle σ of H 0 ⊗ H 0 to A satisfying that there is an isomorphism π of A σ H 0 onto B, which is the twisted crossed product of A by the weak action of H 0 on A and the unitary cocycle σ , such that F = E • π, where F is the canonical conditional expectation from A σ H 0 onto A.