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This paper presents an algorithm for variable ordering for Taylor Expansion Diagrams (TEDs). First we prove that the function implemented by the TED is independent of the order of its variables, and then that swapping of two adjacent variables in a TED is a local permutation similar to that in BDD. These two properties allow us to construct an algorithm to swap variables locally without affecting the entire TED. The proposed algorithm can be used to perform dynamic reordering, such as sifting or window permutation. We also propose a static ordering that can help reduce the permutation space and speed up the search of an optimal variable order for TEDs.