Abstract-The propagation characteristics of electromagnetic waves at the interface between an isotropic regular medium and an anisotropic metamaterial for arbitrary orientation of principal axis are investigated. In terms of the different sign combinations of the tensor components along principal axes, the anisotropic media are divided into four classes. The existence conditions of negative refraction are discussed in different cases, indicating that the conditions for the existence of negative refraction are closely dependent on the principal components and the rotation angle. Furthermore, the influence of the rotation of the principal axes on the incident angle region is analyzed for each case, and the optimal material parameters are attained for the maximum area of the incident angle region of negative refraction occurrence.