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A novel approach to achieving microwave frequency multiplication with a continuously tunable multiplication factor using an unbalanced temporal pulse shaping (TPS) system is proposed and demonstrated. The proposed TPS system consists of a Mach-Zehnder modulator and two dispersive elements having opposite dispersion values. Since the values of dispersion are not identical in magnitude, the entire system can be considered as a typical balanced TPS system for a real-time Fourier transformation followed by a residual dispersive element for a second real-time Fourier transformation. The microwave frequency multiplication factor is determined by the dispersion values of the two dispersive elements and can be continuously tunable by changing the values. Numerical simulations and experiments are performed. Microwave frequency multiplication with a factor as high as 13.2 is experimentally demonstrated.