Previous coupled mode approaches to acoustic propagation in ocean waveguides either (1) apply strictly to the case where interfaces other than the (free) ocean surface are range‐independent, or else (2) they satisfy the boundary conditions at such interfaces approximately. In this paper coupled mode theory is extended to give a solution which exactly satisfies the boundary condition on a range‐varying rigid basement. This is achieved by transforming the coordinate system so that at each range the basement coincides with a coordinate surface, and the partial separation of variables is construed with respect to the coordinate that is normal to that surface. Related work by other researchers is discussed, and the numerical implementation of the theory is described. Results for basements exhibiting both upsloping and downsloping regions are presented and discussed.