  We find a counterexample to a conjecture of Ga{\l}\k{e}ski by constructing
for some positive integers $m<n$ a mapping $f\in
C^1(\mathbb{R}^n,\mathbb{R}^n)$ satisfying $\mathrm{rank}\, Df\leq m$ that,
even locally, cannot be uniformly approximated by $C^2$ mappings
$f_\varepsilon$ satisfying the same rank constraint $\mathrm{rank}\,
Df_\varepsilon\leq m$.
