  The Skorokhod map is a convenient tool for constructing solutions to
stochastic differential equations with reflecting boundary conditions. In this
work, an explicit formula for the Skorokhod map $\Gamma_{0,a}$ on $[0,a]$ for
any $a>0$ is derived. Specifically, it is shown that on the space
$\mathcal{D}[0,\infty)$ of right-continuous functions with left limits taking
values in $\mathbb{R}$, $\Gamma_{0,a}=\Lambda_a\circ \Gamma_0$, where
$\Lambda_a:\mathcal{D}[0,\infty)\to\mathcal{D}[0,\infty)$ is defined by
\[\Lambda_a(\phi)(t)=\phi(t)-\sup_{s\in[0,t]}\biggl[\bigl(\
phi(s)-a\bigr)^+\wedge\inf_{u\in[s,t]}\phi(u)\biggr]\] and
$\Gamma_0:\mathcal{D}[0,\infty)\to\mathcal{D}[0,\infty)$ is the Skorokhod map
on $[0,\infty)$, which is given explicitly by
\[\Gamma_0(\psi)(t)=\psi(t)+\sup_{s\in[0,t]}[-\psi(s)]^+.\] In addition,
properties of $\Lambda_a$ are developed and comparison properties of
$\Gamma_{0,a}$ are established.
