Abstract. Analysis of published data on the third- and fourth-order moments of vertical velocity in the atmospheric boundary layer is performed, and it is shown that turbulence is non-Gaussian even when almost symmetric. It is also proposed that the relationship between third- and fourth-order moments depends on stability. New data from a wind tunnel experiment roughly support this hypothesis. The analysis presented can explain some differences among datasets, and provides a starting point for investigation on the dependence of third- and fourth-order moments on stability.