Theoretical values of site attenuation for broadband receiving antenna or the antenna factor of broadband antenna over the frequency range from 30 MHz to 1 GHz have been calculated or measured by some researchers. For a frequency range over 1 GHz, wire antennas or horn antennas should be used. However, the theoretical site attenuation or antenna factor over 1 GHz have never yet been calculated. A CLS (Conical Log-periodic Spiral) antenna is generally used for EMC/EMI measurements in the microwave band as a broadband wire antenna for the swept frequency method. However, this antenna has the defect that its use results in the loss of polarization information. So we proposed an improved CLS antenna which has linear polarization. This new CLS antenna has another wire wound symmetrically to that of the standard CLS antenna. For this reason, we named it a double-wire CLS antenna. The double-wire CLS antenna loses no polarization information. We calculated the height pattern and the frequency characteristics of CSA (Classical Site Attenuation) for the double-wire CLS antenna when used for receiving, or used for both transmitting and receiving, as well as the antenna factor. Moreover, NSA (Normalized Site Attenuation) when the double-wire CLS antenna is used for receiving or used for both transmitting and receiving in free space were calculated.