Let 𝑛 ≥ 2. A continuous 𝑛-linear form 𝑇 on a Banach space 𝐸 is called norm-peak if there is a unique (𝑥1, … , 𝑥𝑛) ∈ 𝐸𝑛 such that ║𝑥1║ = … = ║𝑥𝑛║ = 1 and for the multilinear operator norm it holds ‖𝑇 ‖ = |𝑇 (𝑥1, … , 𝑥𝑛)|.Let 0 ≤ 𝜃 ≤ = ℝ2 with the rotated supremum norm ‖(𝑥, 𝑦)‖(∞,𝜃) = max {|𝑥 cos 𝜃 + 𝑦 sin 𝜃|, |𝑥 sin 𝜃 − 𝑦 cos 𝜃|}.In this note, we characterize all norm-peak multilinear forms on . As a corollary we characterize all norm-peak multilinear forms on = ℝ2 with the 𝓁𝑝-norm for 𝑝 = 1, ∞.