The three‐dimensional (3‐D) instability of a parallel mean flow and a two‐dimensional (2‐D) wave is examined. Such secondary instability is shown to exist for the Gaussian profile as a model for the wake. Numerical results are obtained based upon a recently proposed wave–mean‐flow interaction mechanism, with the assumptions of temporal problem and inviscid flows. Classical 2‐D instability is strong in the near wake but decays to zero in the far wake, where it is overwhelmed by 3‐D instability. It is conjectured that this will qualitatively explain the emergence of three‐dimensionality in the far wake.