In dimension n ≥ 3, we prove a local uniqueness result for the potentials q of the Schrödinger equation −∆u + qu = 0 from partial boundary data. More precisely, we show that potentials q 1 , q 2 ∈ L ∞ with positive essential infima can be distinguished by local boundary data if there is a neighborhood of a boundary part where q 1 ≥ q 2 and q 1 ≡ q 2 .