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Abstract In this paper, a class of sixth-order finite difference schemes for the Helmholtz equation with inhomogeneous Robin boundary condition is derived. This scheme is based on the sixth-order approximation for the Robin boundary condition by using the Helmholtz equation and the Taylor expansion, by which the ghost points in the scheme on the domain can be eliminated successfully. Some numerical examples are shown to verify its correctness and robustness with respect to the wave number.