The frequency diverse arrays (FDAs) have been extensively investigated since it can provide a unique angle‐range‐dependent beampattern. This range‐dependent characteristic can suppress the range ambiguous clutters, leading to many novel potential Radar applications. Two issues, however, exist in conventional FDA (CFDA) beampatterns, that is, range‐angle coupling and range periodicity. Therefore, for a CFDA Radar, target range information cannot be obtained directly from the beampattern peaks and target ambiguity occurs in the range domain. In this work, a new frequency diverse array (FDA) transmitter architecture with random logarithmically increasing frequency offset (log‐RFDA) is presented. It is shown that the proposed strategy provides a nonperiodic thumbtack‐like beampattern, eliminating the ambiguity in range domain, suffered in the CFDA Radar. Furthermore, reduced side lobe and higher detection resolution can be achieved, compared with the previously reported log‐FDA.