The nonlinear crystal with sharp-step dependence of dielectric function on the electric field covered by shielding thin film is considered. A change in the signs of the nonlinearity coefficient is induced by the electric field. Different sets of boundary conditions are used to calculate the exact solutions of the formulated equation. New types of nonlinear surface waves are found and the conditions of their existence are derived analytically. In certain cases, some types of surface waves are characterised by free-varying wave frequency and effective refractive index. Other types of surface waves can propagate with a certain effective refractive index and arbitrary frequencies. In addition, new types of waves propagating only with fixed effective refractive index and fixed frequency are described.