Abstract: The direct formulation of quadrilateral plane element in rectangular Cartesian coordinate system has been a forbidden zone for finite element method.In this paper,the quasi-conforming finite element method is applied on this problem and a bilinear element as well as complete second-order element is constructed.Meanwhile,the convergence analysis of the elements is carried out with "Taylor expansion test" and the comparative study with isoparametric element is also considered.The results show the direct formulation of quadrilateral plane elements is feasible within the quasi-conforming framework,and there is not any convergence problem with these elements.Therefore the finite element theory concerning plane element can be unified by quasi-conforming framework.Compared with isoparametric elements,the bilinear element present in this paper is easy to formulate,with stable performance and explicit stiffness matrix for the plane problem analysis.