One of the standard products which induces a structure of an algebra on

${M}_{n}$, the space of all

$n\times n$ complex matrices, is the Lie product

$[A,B]=AB-BA$,

$A,B\in {M}_{n}$. Every Lie automorphism of

${M}_{n}$ has a nice form. Recently,

*P. Šemrl* [Acta Sci. Math. 71, No. 3–4, 781–819 (2005;

Zbl 1111.15002)] and the author [Publ. Math. 71, No. 3–4, 467–477 (2007;

Zbl 1164.17015)] obtained a characterization also for non-linear Lie homomorphisms. Let

$F$ be an arbitrary field with characteristic zero, let

${T}_{n}$ be the Lie algebra of all

$n\times n$ upper triangular matrices over

$F$. It is the aim of this study to characterize maps which preserve the Lie product on

${T}_{n}$. We can construct various maps on higher-dimensional algebras of upper triangular matrices which preserve the Lie product. If we assume that the map on

${T}_{n}$ which preserves Lie product is bijective, then we can obtain a nice characterization.