Workflow verification is an important and complex step in workflow analysis and design. Further, certain classes of workflow models can contain cycles, thus making workflow verification even more challenging. Few commercial workflow systems have implemented the workflow verification functionality, partly due to the lack of simple, yet generic algorithms that can handle cyclic processes. We have developed an innovative method that views a cycle as the composition of a main path and a feedback path. Based on this perspective, we develop ways to identify the cycles and determine the feedback path in each elementary cycle. Furthermore, our previous research results on matrix-based workflow abstraction and verification for acyclic processes can be extended to verifying cyclic workflows. We refer to our method of dealing with cycles as Feedback Identification and Partition (FIP). In this paper, we present the basic FIP concept and algorithms, prove the theoretical correctness of the FIP approach, and demonstrate the use of the FIP method in a real world example.