Wrinkding is a commonly observed out-of-plane instability in membrane structures due to theirextremely low bending-to-stretching stiffness ratio. It has been extensively investigated for symmetricmembrane geometries and boundary conditions that induce planar non-uniform stress states by preventing thelateral contraction at the edges, and are also known to potentially display self-restabilization. This presentationoutlines a recent investigation into an initially flat, parallelogram-shaped hyperelastic membrane, focusing onthe influence of the inclination angle defining the membrane shape as a deviation from the rectangulargeometry. It is shown that wrinkding can occur either centrally or at the two opposite obtuse-angled corners-ven for small inclination angles-during stretching with unconstrained lateral contraction, a condition underwhich the flat configuration for the rectangular counterpart remains always stable. Three distinct evolutions ofthe wrinkding pattern are numerically identified, all ultimately leading to corner localized wrinkdes. This finalstate may arise (i) directly, without a prior bifurcation, or after the appearance of central wrinkding that eitherii) restabilizes or (ii) separates and migrates toward the corners. A closed-form expression for the criticalwrinking condition is derived by combining a perturbation approach with an energy-based method in theframework of linear elasticity. This provides an accurate estimate of the onset and pattern of central wrinkding.The present findings reveal new pathways in wrinkding pattern evolution and introduce a novel approach tounconventional boundary value problems, with potential applications ranging from lightweight structural systemsto flexible electronics.