A hybrid stress quadrilateral macro-element HQM is proposed. Compatible linear displacements are used on its two triangular sub-domains, and a 5-parameter incomplete linear stress mode is suggested. Equivalence to another quadrilateral element HQ4 with compatible isoparametric bilinear displacements is proven. Due to elimination of stress parameters at the element level, the computational cost of HQM/HQ4 is as same as that of Q4. Numerical tests show that the element is accurate, insensitive to mesh distortions, and free from Poisson locking.