Water wave propagation over uneven bottom with large oblique radiation is considered and solved by the fourth-order radiation boundary condition which involves a fifth-order mixed derivative.A coupled equation approach is utilized to split the high-order mixed derivatives into coupled lower-order ones which are then solved by the local radial-basis-function collocation method(LRBFCM)based on the multiquadric radial basis function.When treating the mixed derivatives,the basis function can be straightforwardly differentiated.Numerical results based on the fourth-order radiation boundary condition are found to be in a better agreement than those of the lower-order radiation boundary conditions especially for large radiation angles.Overall,we apply the LRBFCM for approximating the fourth-order radiation boundary condition of the water wave problems.The method is simple,meshless and free from integrations.Furthermore,the present method can be combined with other numerical methods,such as the finite difference and finite element methods.This will be very helpful if the radial-boundary-condition approximation of a well-established code is replaced by the present method.