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Composite laminates with negative Posson's ratios (i.e., auxetic composite laminates) were experimentally found to demonstrate a three-fold increase in buckling strength under uniaxial compression in comparison with the equivalent non-auxetic ones. To investigate whether the enhancement is genuinely due to the negative Poisson's ratio (i.e., the auxeticity) or merely caused by the concurrent change in the bending stiffness matrix as the composite layup changes, a novel monoclinic plate-based composite laminate approach is proposed, which for the first time, allows to isolate the auxeticity effect from the concurrent change of the stiffness matrix. Results provided theoretical proof that the auxeticity plays an active role in enhancing the critical buckling strength of layered composite structure. However, such a role is dynamically sensitive to elements in the bending stiffness matrix, especially the bending-twisting ratio and the anisotropy of the bending stiffness between the longitudinal and lateral directions. Insights are expected to provide guidance in exploiting negative Poisson's ratio for improving the stability of layered composite structures.