  The square of a graph is obtained by adding additional edges joining all pair
of vertices of distance two in the original graph. Particularly, if $C$ is a
hamiltonian cycle of a graph $G$, then the square of $C$ is called a
hamiltonian square of $G$. In this paper, we characterize all possible
forbidden pairs, which implies the containment of a hamiltonian square, in a
4-connected graph. The connectivity condition is necessary as, except $K_3$ and
$K_4$, the square of a cycle is always 4-connected.
