  Given an $m$-component link $L$ in $S^3$ ($m \ge 2$), we construct a family
of links which are link homotopic, but not link isotopic, to $L$. Every proper
sublink of such a link is link isotopic to the corresponding sublink of $L$.
Moreover, if $L$ is an unlink then there exist links that in addition to the
above properties have all Milnor invariants zero.
