New impedance boundary conditions (IBC) difference schemes are proposed for wide-angle shift-map PE. A simple experiment is set up to check the accuracy of the PE. We explain the drawbacks of original boundary conditions (BCs) difference schemes. Some problems are caused by the PEC boundary. We use one-sided difference schemes for the BCs as substitutes. The proposed schemes not only meet the physical property but also perform well in numerical calculation. The numerical experiments are done on PEC and media boundaries to study the characteristic of the new BCs. The reflection calculated by PE are compared with Fresnel reflection. The numerical analysis reveals that the new BCs scheme errors are smaller than those of the original BCs. The new 1st-order PE is accuracy for the slope up to 14° with the reflection angle offset being less than 0.5°, where a horizontally spreading, 0.5° beamwidth levy source illuminates the slope. Under the same condition, the 2nd-order Claerbout PE is accurate when the slope is less than 16° and the 2nd-order Greene PE is accurate when the slope is less than 19°. In addition, the ripples caused by the 2nd-order PE with new BCs is smaller than the original one.