We investigated experimentally the dynamics of the three-dimensional secondary instability developing in the wake of a thin flat plate at moderate Reynolds numbers. The wake is formed as the two laminar boundary layers developing on each side merge at the trailing edge of the flat plate. Both the spatial and temporal evolution of the two- and three-dimensional instabilities are analysed by means of laser-induced visualizations of the deformation of the interface separating the two streams. It was found that although the wake may exhibit two distinct three-dimensional modes with different symmetry characteristics, Modes 1 and 2 (Lasheras & Meiburg 1990), the latter appears to be amplified first, thereafter dominating the evolution of the near wake. By varying the forcing frequency of the primary two-dimensional instability, we found that the wavelength of the three-dimensional mode is selected by the wavelength of the two-dimensional Kármán vortices, with a ratio ($(\l_{3D}/\l_{2D})$) of order one. In the far-wake region, both modes appear to grow and co-exist. Furthermore, by analysing the response of the wake to spanwise-periodic and impulsive perturbations applied at the trailing edge of the plate, we demonstrate that the nature of the secondary instability of the wake behind a thin flat plate is convective. In addition, both modes are shown to have comparable wavelengths and to be the result of the same instability mechanism.