Business process management system such as workflow management system has attracted increasing research attentions in e-commerce, especially from an inter-organizational workflow perspective. When designing inter-organizational workflow, it is important to consider soundness of the workflow, which identifies whether a workflow terminates properly. The principle of local criteria ensuring global soundness can be applied to allow the soundness of the entire inter-organizational workflow to be achieved without knowing the detail workflow of every participating organization. However, this principle sometime can become too restrictive when we attempt to ensure the overall workflow is sound while changes are made to the workflow. It is not always easy to reach a balance between achieving soundness and flexibility. This paper presents an approach to make the public-to- private approach more flexible by proposing a weakly equivalence concept in an inter- organizational workflow context that can function as a local criterion.