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<jats:title>ABSTRACT</jats:title> <jats:p>Using the five-year <jats:italic>WMAP</jats:italic> data, we re-investigate claims of non-Gaussianities and asymmetries detected in local curvature statistics of the one-year <jats:italic>WMAP</jats:italic> data. In Hansen et al., it was found that the northern ecliptic hemisphere was non-Gaussian at the ∼1% level testing the densities of hill, lake, and saddle points based on the second derivatives of the cosmic microwave background temperature map. The five-year <jats:italic>WMAP</jats:italic> data have a much lower noise level and better control of systematics. Using these, we find that the anomalies are still present at a consistent level. Also the direction of maximum non-Gaussianity remains. Due to limited availability of computer resources, Hansen et al. were unable to calculate the full covariance matrix for the χ<jats:sup>2</jats:sup>-test used. Here, we apply the full covariance matrix instead of the diagonal approximation and find that the non-Gaussianities disappear and there is no preferred non-Gaussian direction. We compare with simulations of weak lensing to see if this may cause the observed non-Gaussianity when using a diagonal covariance matrix. We conclude that weak lensing does not produce non-Gaussianity in the local curvature statistics at the scales investigated in this paper. The cause of the non-Gaussian detection in the case of a diagonal matrix remains unclear.</jats:p>