  We complete characterization of bijections preserving commutators (PC-maps)
in the group of unitriangular matrices $UT(n,F)$ over a field $F$, where $n$ is
a natural number or infinity. PC-maps were recently described up to almost
identity PC-maps by M.Chen, D.Wang, and H.Zhai (2011) for finite $n$ and by
R.Slowik (2013) for $n=\infty$. An almost identity map is a map, preserving
elementary transvections. We show that an almost identity PC-map is a
multiplication by a central element. In particular, if $n=\infty$, then an
almost identity map is identity. Together with the result of R.Slowik this
shows that any PC-map of $UT(\infty, F)$ is an automorphism.
