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A new design of dual band compact microstrip antenna is proposed for Ku-band applications. Dual band is achieved using three pairs of thin slits from the sides of a rectangular patch and feeding with a microstrip feedline. The antenna has a compact structure and the total size is 9.50 mm by 10 mm by 0.254 mm. The result shows that the return loss of -23.83 dB is achieved at the first resonant frequency of 12.54 GHz and -14.04 dB is obtained at the second resonant frequency of 14.15 GHz. The antenna gives a stable radiation performance with gain greater than 4 dBi over the frequency band.