In a previous paper a modified Hu-Washizu variational formulation has been used to derive an accurate four node plane strain/stress finite element denoted QE2. For the mixed element QE2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case. In this paper an alternative approach is discussed. The new formulation leads to the same accuracy for linear elastic problems as the QE2 element; however it turns out to be more efficient in numerical simulations, especially for large deformation problems. Using orthogonal stress and strain functions we derive B functions which avoid numerical inversion of matrices. The B -strain matrix is sparse and has the same structure as the strain matrix B obtained from a compatible displacement field. The implementation of the derived mixed element is basically the same as the one for a compatible displacement element. The only difference is that we have to compute a B -strain matrix instead of the standard B-matrix. Accordingly, existing subroutines for a compatible displacement element can be easily changed to obtain the mixed-enhanced finite element which yields a higher accuracy than the Q4 and QM6 elements.