This paper is a mathematical analysis of a new type of phaseswitched radar which uses four antennae, two for transmitting and two for receiving. By phase-switching the pulses of one of the transmitting antennae and by multiplicative detection of the outputs from the two receiving antennae one can obtain a two-way power pattern proportional to the product of the four directivity (field strength) patterns of the system's four antennae. Furthermore, by appropriate phase and amplitude switching of a single array's element currents it is possible to simulate four coincident arrays whose product pattern can be obtained. The greater flexibility of this system (four pattern functions instead of one) is demonstrated byexamples of improved pattern synthesis. Comparison is made with a conventional array of the same size whose pattern beam-width is the same as that of the phase-switched system; the phase-switched pattern has lower side-lobes and four times as many nulls. The effect of uncorrelated element noise and of a second target (either coherent or incoherent) is also considered. It is shown that for any degree of coherence one can synthesize a better pattern with the phase-switched system.