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In this paper, a new quadrilateral 5-node non-conforming membrane element with drillingdegrees of freedom is presented. The main advantage of these elements is the relatively small number ofintegration points to evaluate a stiffness matrix comparing to the existing transition membrane elements(CLM elements). Moreover, the presented elements pass the patch test by virtue of the DirectModification Method incorporated into the element formulation. The presented 5-node elements areproved to be very efficient when used in the local mesh refinement for the in-plane structures which havestress concentrations. And some numerical studies also show the good performance of the new elementdeveloped in this study.