The decay of a grooved profile when the average orientation is singular is treated in the particular case when the orientations close to the singular one are unstable. The system is assumed to exchange atoms with its vapour. The step fluctuations, which allow the profile decay, are treated by a partially exact transfer matrix method. The time τ to peel the topmost layer is obtained as a function of the width l of a terrace: τ lexp(kl), where the constant k depends on the temperature.