The potential vorticity on isentropic surfaces is used to study a characteristic type of upper-level frontogenesis — the development of a sloping stable layer marked by strong vertical wind shear and rapid upward decrease in humidity. In the case studied it was found that the intense portion of the frontal zone consisted of a thin wedge of stratospheric air which had descended to very low levels (700 to 800 millibars), the frontal boundaries being a folded portion of the original tropopause. The circulation within the frontal zone was indirect solenoidal, and surface cyclogenesis accompanied or slightly preceded the strengthening of the upper-level front. Although the frontal zone formed entirely within a polar air-mass, the strong adiabatic heating at and near the warm boundary could give the false impression that tropical air was present there at the end stage.