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A numerical model of five-order mode converter that converts the order of modes in an integrated-optic multimode waveguide is proposed. Such a structure is useful in optical guiding wave devices for mode control and mode shuffling. The dimensions and index profile of the device are well within the capabilities of the state of the art of integrated optics technology. We have successfully optimized the structural design of the device for propagation loss of less than 13.1 dB at an operating wavelength of 1.55 μm. A cascaded form of the five-order mode converter is also proposed for selective mode conversion without the need of restructuring the connection within the device.