In recent published papaers [3], [4] and [5] concepts of normal, dually normal, conjugative and dually conjugative relations are introduced and analzyed by Jiang Guanghao, Xu Luoshan, Cai Jin and Han Guiwen In this paper, as ilustration of the concept applied in mentioned papers, normal relations on a poset, introduced in article [5], is analyzed. A characterizations of normal relations are obtained. In addition, particulary we show when the anti-order relation $\leq^{\operatorname{C}}$ is normal.