An aspect of the stability of boundary‐layer profiles containing a point of zero shear away from the wall is examined. Analysis of a viscous critical layer at the point of zero shear shows that the classical unsteady boundary‐layer equation contains a short‐wavelength unstable solution. The presence of this instability has consequences for the numerical solution of the classical boundary‐layer equation, and may be connected with the initiation process of Van Dommelen and Shen’s nonlinear unsteady separation singularity.