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In this letter, a triangular monopole on a fractal-based ground plane is designed to obtain a dual-band antenna for the 802.11 standard (WLAN). The ground plane is based on a mod-2 Sierpinski gasket repeated four times and rotated to obtain a square ground plane. The operating bands of the antenna are adjusted using the height of the monopole, the dimensions of the ground plane and the scale factor used to create the fractal shape. Simulations and measurements are in good agreement showing the advantages of using the fractal-based ground plane instead of the solid ground plane.