Fix an algebraic space $S$ , and let ${\mathcal X}$ and ${\mathcal Y}$ be separated Artin stacks of finite presentation over $S$ with finite diagonals (over $S$ ). We define a stack $\underline{\rm Hom}_S({\mathcal X}, {\mathcal Y})$ classifying morphisms between ${\mathcal X}$ and ${\mathcal Y}$ . Assume that ${\mathcal X}$ is proper and flat over $S$ , and assume fppf locally on $S$ that there exists a finite finitely presented flat cover $Z\rightarrow {\mathcal X}$ with $Z$ an algebraic space. Then we show that $\underline{\rm Hom}_S({\mathcal X}, {\mathcal Y})$ is an Artin stack with quasi-compact and separated diagonal