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In recent years, frequency diverse array radar with fixed frequency offset has been proposed and investigated. It has been shown that the beampattern of this category of radar is time-dependent as well as range-angle-dependent. In this letter, we have proposed time-dependent frequency offset to achieve a beampattern that is time-independent for a given pair of range and angle. The proposed radar system has been analyzed mathematically, and the simulation results are presented. Simulations show that the beampattern does not change with time for a particular range-angle pair, but it remains time-dependent for other values of range and angle. With the proposed radar system, the target remains illuminated constantly for the whole pulse duration, causing a high-energy reflection that can increase detectability of the target.