Descent properties of hermitian Witt groups in inseparable extensions

Let k be a field of characteristic ≠ 2, A be a central simple algebra with involution σ over k and W(A, σ) be the associated Witt group of hermitian forms. We prove that for all purely inseparable extensions L of k, the canonical map ({r_{L/k}: W(A, sigma) longrightarrow W(A_L, sigma_L)}) is an isomorphism.