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This letter studies the interference between the even and the odd subchannels in the interleaved multiplexing optical fast orthogonal frequency-division multiplexing system, which is caused by the non-orthogonal demultiplexing transform at the receiver. To eliminate this interference, frequency and timing offsets are introduced deliberately at the receiver to form orthogonal bases, which coincide with the discrete cosine and sine transforms of type-IV. Thus, the symbols can be demultiplexed at the receiver without any interference between subchannels, and the proposed receiver design can be implemented efficiently. Finally, analysis and simulation are provided to verify its feasibility and the ability to eliminate such interference.