A uniform asymptotic high-frequency solution is developed for the diffraction of plane waves ? by an acoustically transmissive strip located between two half-planes which are soft at the top and ?hard at the bottom. After simulating the partially transmissive strip by a set of approximate boundary ?conditions used recently by Rawlins et al., the three-part boundary value problem is formulated into ?a ''modified matrix Wiener-Hopf equation''. By performing the factorization of the kernel matrix ?through the Daniele-Khrapkov method, the modified matrix Wiener-Hopf equation is first reduced ?to a pair of coupled Fredholm integral equations of the second kind and then solved by iterations. An ?interesting feature of the present solution is that the classical Wiener-Hopf arguments yield unknown ?constants that can be determined by means of the edge conditions.