Fracture zones in the world's oceans appear clearly in the Seasat altimeter (geoid) data wavelength of about 100 km and less. In the North and South Atlantic these signatures are stable in form and amplitude from the ridge crest to crust tens of millions of years old and can be mapped across nearly the width of the basin. The signatures diminish in amplitude markedly on crust older than 70 to 80 m.y. B.P., apparently when thickly covered by sediments. Because fracture zone trajectories closely approximate plate motion flow lines, they may be used to infer the plate kinematic history of the ocean basin. In this paper I describe a new method for estimatig the relative poles of opening, describing the history of motion between two plates by using fracture zone trajectories. The method is an iterative inversion whereby the trajectories of synthetic flow lines are linearized with respect to the pole parameters. When applied to the Seasat altimeter track data, a waveform inversion based upon this method is possible in which the altimeter data are modeled using a synthetic geoid fracture zone signal. This waveform inversion is applied to 17 prominent fracture zones in the central and South Atlantic to estimate the poles of opening between the South American and African plates. Altogether, 1022 Seasat fracture zone crossings are used; for each of these a waveform comparison is made. The new method of found to be robust and convergence to a stable set of pole solutions even if the initial flow lines are small circles about a single pole that poorly approximates the observed trajectories. The solution poles document a Cenozoic change in plate motion near anomaly 13 time (36 m.y. B.P.) similar to that in the North Atlantic at anomaly 13--21 time (36--50 m.y. B.P.). ¿ American Geophysical Union 1987