We report the detection of small scale bending waves, also known as corrugations, in the dust lanes of five nearby edge-on disc galaxies. This phenomenon, where the disc mid-plane bends to become wavy, just as in warps but on a smaller scale, is seen here for the first time, in the dust lanes running across the discs. Because they are seen in absorption, this feature must be present in the dust disc in the outskirts of these galaxies. We enhance the visibility of these features using unsharp masking, trace the dust mid-plane across the disc, measure the corrugation amplitude by eye and the corrugation wavelength using Fourier analysis. The corrugation amplitude is found to be in the range of 70 - 200 pc and the wavelengths lie between 1 - 5 kpc. In this limited sample, we find that the amplitude of the corrugations tends to be larger for lower mass galaxies, whereas the wavelength of corrugation does not seem to depend on the mass of host galaxies. Linear stability analysis is performed to find out the dynamical state of these dust discs. Based on WKB analysis, we find that the dust corrugations in about half of our sample are stable. Further analysis, on a larger sample would be useful to strengthen the above results.