A numerical scheme of integration is devised to integrate the unsteady laminar boundary‐layer equations with partly reversed flows. The neighborhood of the vanishing skin friction which has been considered up to now as the location of separation, is found to be nonsingular while a typical Goldstein‐type of a traveling singularity is discovered farther downstream. This singularity is interpreted according to the theory of Sears and Telionis as unsteady boundary‐layer separation. The features of the flow in the neighborhood of the singularity are investigated.