In the present paper a modified rectangular patch antenna is proposed to achieve compact size, broadband and dual frequency performance. The proposed antenna is designed to function in the median band (3.25 to 3.85 GHz) of WiMax systems, following standards created by IEEE 802.16 Working Group. The proposed antenna designed on glass epoxy FR-4 substrate is radiating at two different Frequencies 3.49 GHz and 3.68 GHz without much loss in its radiation performance. The impedance bandwidth of the antenna is 8.75%. The radiation patterns in the entire range of interest of frequencies are identical in shape.