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This letter demonstrates a novel method to generate high-purity optical millimeter-wave signals with carrier suppression by using a frequency quadrupling technique. To the authors' knowledge, this is the first time that a frequency quadrupling system requires only a single integrated Mach-Zehnder modulator without a narrowband optical filter to remove undesired optical sidebands. Since no optical filter is needed, fast frequency tuning is straightforward and this approach will be particularly attractive for optical up-conversion in wavelength-division-multiplexing radio-over-fiber systems. This letter provides both theoretical analysis and experimental demonstration. The generated optical millimeter-wave signals have very high quality with an optical carrier and harmonic distortion suppression ratio of more than 38 and 36 dB at 40 and 72 GHz, respectively.