  Let $\omega$ denote an area form on $S^2$. Consider the closed symplectic
4-manifold $M=(S^2\times S^2, A\omega \oplus a \omega)$ with $0<a<A$. We show
that there are families of displaceable Lagrangian tori $L_{0,x},\, L_{1,x}
\subset M$, for $x \in [0,1]$, such that the two-component link $L_{0,x} \cup
L_{1,x}$ is non-displaceable for each $x$.
