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In this work, log-periodic antennas with improved cross-polarization level were studied. It was found that some modifications of the traditional design lead to an essential improvement of the co-to-cross polarization ratio up to 40 dB. An improved design of a log-periodic dipole antenna with low cross-polarization level is described. Some recommendations regarding improvement of the polarization characteristics of log- periodic antennas in general are also given. It was also found that log-periodic antennas can be attributed to the class of so-called first-order (m = plusmn1) antennas, which is an important requirement for probes in spherical near- field antenna measurements.