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A new approach employing infinite order boundary conditions is used to obtain an approximate solution of the problem of the scattering of a surface wave by a step in a grounded dielectric slab. The infinite order boundary conditions are used to replace certain continuity and boundary conditions in the exact problem and to reduce the exact problem to one amenable to the Wiener-Hopf technique. The basis of construction of the infinite order boundary conditions is described, and the criteria governing their application given. The reformulated problem is solved for various parameter values and compared with the results obtained by a variational technique.