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Wide frequency band antenna systems are required for many now and future applications, such as in radio astronomy and ultrawideband (UWB) technology. Constant radiation characteristics over a decade bandwidth are required for some of wide band applications, for example, feeds for reflector antennas in radio telescope. The log-periodic array antenna is one of the technologies for wideband antennas. In the present paper, an analysis on condition for constant radiation characteristics over wide bandwidth for a log-periodic array antenna is presented. From this condition, a guide rule for designing a wideband log-periodic array antenna is obtained. The Eleven antenna, a decade bandwidth log-periodic array antenna, is selected to illustrate the condition and verify the analysis in the paper.