By means of self-consistent numerical simulations we investigated the dynamical impact of classical bulges on the growth of the secondary buckling of a bar. Overall we considered 14 models with different disc and bulge parameters. We obtained that a bulge with a quite modest mass B/D = 0.1 leads to completely symmetrical evolution of the bar almost independently of the initial stellar disc parameters and even can damp the first bending. At the same time, the bars in all our bulgeless models suffer from the short primary and prolonged secondary buckling. Given the smallness of the mass suppressing secondary buckling, we conclude that a classical bulge along with the gas central concentration may be the main culprits for the rarity of bars with ongoing buckling in the local Universe.