A new wedge diffraction function, called as Naveed-Naqvi-Hongo (NNH) wedge diffraction function, is derived and evaluated asymptotically by applying the steepest descent method. It is found that the total field with NNH solution is continuous at the shadow boundaries and gives the well known non-uniform expression for the observa- tion point far from the shadow boundaries. Numerical comparison of NNH solution is made with exact series solution and Pauli-Kouyumjian-Pathak (PKP) result. It is found that the agreement among these three is fairly well. In contrast to the ex- pressions proposed by Kouyoumjian and Pathak, the NNH solution does not need the parameters to switch for the region of validity, hence it is easier to make a numerical code. The validity of NNH wedge diffraction function is further checked by evaluating the diffracted field from a geometry which contains an infinite slit in a perfect electric conducting (PEC) plane. It is further extended to a more complex geometry consisting of two parallel PEC wedges and a perfect electromagnetic conductor (PEMC) circular cylinder which is placed under the PEC wide double wedge. It is found that by using the NNH solution, the results evaluated for some special cases, including the trans- mission coefficient of PEC slit, are in fairly good agreement with the published work. The transmission coefficient and the diffraction pattern of PEC wide double wedge is studied and elaborated by considering a geometry consisting of a coated PEMC cylin- der placed under the two parallel wedges. The cylinder is coated with double positive (DPS) or double negative (DNG) materials. Finally, a comparison of the transmission coefficient of PEC geometry, as evaluated by using NNH solution, is made with the geometry of more practical nature, that is, an impedance slit