Suppose F is an arbitrary field. Let ${mid}F{mid}$ be the number of the elements of F. Let $T_{n}(F)$ be the space of all $n{ imes}n$ upper-triangular matrices over F. A map ${Psi};:;T_{n}(F);{ ightarrow};T_{n}(F)$ is said to preserve idempotence if $A-{lambda}B$ is idempotent if and only if ${Psi}(A)-{lambda}{Psi}(B)$ is idempotent for any $A,;B;{in};T_{n}(F)$ and ${lambda};{in};F$. It is shown that: when the characteristic of F is not 2, ${mid}F{mid};>;3$ and $n;{geq};3,;{Psi};:;T_{n}(F);{ ightarrow};T_{n}(F)$ is a map preserving idempotence if and only if there exists an invertible matrix $P;{in};T_{n}(F)$ such that either ${Phi}(A);=;PAP^{-1}$ for every $A;{in};T_{n}(F);or;{Psi}(A)=PJA^{t}JP^{-1}$ for every $P;{in};T_{n}(F)$, where $J;=;{sum}^{n}_{i-1};E_{i,n+1-i};and;E_{ij}$ is the matrix with 1 in the (i,j)th entry and 0 elsewhere.