Abstract: In order to construct quadrilateral elements insensitive to mesh distortion, a new kind of quadrilateral area coordinate method, denoted as QAC-2, has been successfully developed. And related differential and integral formulae are also presented. As a natural coordinate system, QAC-2 has explicit physical meanings. It includes only two independent components, Z1 and Z2, which make it easier to communicate with Cartesian coordinates and isoparametric coordinates. Furthermore, since Z1 and Z2 are linear functions of Cartesian coordinates x and y, it is convenient to establish a polynomial with high order completeness in Cartesian coordinates by using Z1 and Z2, and this polynomial will keep its completeness order invariable for mesh distortion cases. QAC-2 is a simple and novel tool for developing more accurate and robust quadrilateral element models.