<abstract><p>By investigating complete Willmore maximal spacelike hypersurfaces with constant scalar curvature in anti-de Sitter space $ \mathbb{H}_{1}^{5}(-1) $, we give a new characterization of hyperbolic cylinder $ \mathbb{H}^{2}(-2)\times\mathbb{H}^{2}(-2) $ in $ \mathbb{H}_{1}^{5}(-1) $.</p></abstract>