Abstract: The (Euclidean) minimum weight triangulation (MWT) of a planar point set is a long-standing open problem in the fields of computational geometry and algorithm design. Reference 1 presents a new triangulation algorithm, and claims that the algorithm can derive the MWT of a planar point set. By presenting counter-examples, this note proves that the triangulation is not the MWT. So, the problem of the MWT is still open.