  Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{P}_{n}$ be the
semigroup of partial transformations on $[n]$. Let
$\mathcal{CP}_{n}=\{\alpha\in \mathcal{P}_{n}: (for~all ~x,y\in
Dom~\alpha)~|x\alpha-y\alpha|\leq|x-y|\}$, then $\mathcal{CP}_{n}$ is a
subsemigroup of $\mathcal{P}_{n}$. In this paper, we give a necessary and
sufficient condition for an element in $\mathcal{P}_{n}$ to be regular and
characterize all the Green's equivalences on the semigroup $\mathcal{CP}_{n}$.
