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This paper presents a design of a dual frequency microstrip circular patch antenna operating at 2.45 and 5.2 GHz ISM (industrial, scientific, and medical) band. This band is occupied by the applications of Bluetooth and high performance radio local area network (HIPERLAN). The present circular patch antenna has two operating points at the last dual mentioned frequencies. Under the condition of less than 10 dB return loss, the bandwidth at 2.45 is 24 % and at 5.2 is 7.7%. The antenna input impedance is obtained at these frequencies that is very close to 50 Ω so the coaxial cable can be directly connected to it. The radiation pattern of the antenna at the dual frequencies exhibits minimum radiation in the zenith direction and is fairly symmetrical in azimuth that is generally required for this type of applications. The analysis and design of the antenna is carried out using of the finite difference time domain (FDTD) with the perfect matched layer (PML). Verification of the results is obtained by using of the cavity resonance technique and the available published data.