In this talk, we study the $\C$-biharmonicity of a spacelike hypersurface in $\M_1^5(c)$ defined by $\x:M^4\rightarrow\M_1^5(c)$. This condition means that $\x$ satisfies the condition $\C^2\x=0$ which is an extended version of biharmonicity condition $\Delta^2\x=0$, where $\C$ is the Cheng-Yau operator and $\Delta$ is the well-known Laplace operator. We show that if a mentioned hypersurface has at most two distinct principal and constant mean curvature then it is 1-maximal.
