A bi-unitary connection in subfactor theory of Jones producing a subfactor of finite depth gives a 4-tensor appearing in a recent work of Bultinck-Marien-Williamson-Sahinoglu-Haegeman-Verstraete on 2-dimensional topological order and anyons. In their work, they have a special projection called a projector matrix product operator. We prove that the range of this projection of length k is naturally identified with the k-th higher relative commutant of the subfactor arising from the bi-unitary connection. This gives a further connection between 2-dimensional topological order and subfactor theory.