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In this paper the Koch fractal antenna at UHF frequency will be analyzed. In particular, a new technique proposed to adapt the input impedance of the Koch model to be matching with the impedance of the RFID chip. It is important to remark that the proposed technique conserves the same special form of the bi-band Koch dipole model. The Bi-band fractal antenna with input impedance 50 ohms is compared to the new design proposed to be used as a tag RFID. Fractal antennas can obtain both input impedance and radiation pattern similar to a longer antenna, yet take less special area due to the many contours of shape. The fractal antennas (with input impedance equal to 50 ohms) are printed on glass-epoxy FR-4 substrate of thickness 1.6 mm and relative permittivity 4.4. Fractal antennas are a fairly new research area and are likely to have a promising future in RFID applications.