A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper (G.V. Stupakov, Particle Accelerators.), 56, p. 83, 1996 we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems -- a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator. Show Partial Abstract