  Let $L_{k,\alpha}^{\mathbb{Z}}$ denote the set of all bi-infinite
$\alpha$-power free words over an alphabet with $k$ letters, where $\alpha$ is
a positive rational number and $k$ is positive integer. We prove that if
$\alpha\geq 5$, $k\geq 3$, $v\in L_{k,\alpha}^{\mathbb{Z}}$, and $w$ is a
finite factor of $v$, then there are $\widetilde v\in
L_{k,\alpha}^{\mathbb{Z}}$ and a letter $x$ such that $w$ is a factor of
$\widetilde v$ and $x$ has only a finitely many occurrences in $\widetilde v$.
