Abstract: In order to constitute an incompatible element, it is a familiar method to use additional internal parameters based on compatible displacement field. In detail, at present, an incompatible displacement mode (not sure to pass patch test) is assumed firstly, then it is modified by some existent method, so a new incompatible mode which can pass patch test is produced. But these kinds of modifying existent methods are usually complex. From the theory of Generalized Conforming Element, for the first time this paper derives general basic formulations of additional displacement on internal parameters about arbitrary high orders of local coordinates in plane problem, which is simple for engineer to apply in practice. Also, according to these basic formulations, a new incompatible element named Q8λ2on basis of Q8 element is developed in this paper. Numerical examples show feasibility of the basic formulations since this new element can pass patch test, has higher accuracy and less sensitivity to geometric distortion.