  A finite family $\mathcal{F}=\{f_1,\ldots,f_n\}$ of continuous selfmaps of a
given metric space $X$ is called an iterated function system (shortly IFS). In
a case of contractive selfmaps of a complete metric space is well-known that
IFS has an unique attractor \cite{Hu}. However, in \cite{LS} authors studied
highly non-contractive IFSs, i.e. such families
$\mathcal{F}=\{f_1,\ldots,f_n\}$ of continuous selfmaps that for any
remetrization of $X$ each function $f_i$ has Lipschitz constant $>1,
i=1,\ldots,n.$ They asked when one can remetrize $X$ that $\mathcal{F}$ is
Lipschitz IFS, i.e. all $f_i's$ are Lipschitz (not necessarily contractive), $
i=1,\ldots,n$. We give a general positive answer for this problem by
constructing respective new metric (equivalent to the original one) on $X$,
determined by a given family $\mathcal{F}=\{f_1,\ldots,f_n\}$ of continuous
selfmaps of $X$. However, our construction is valid even for some specific
infinite families of continuous functions.
