A wide impedance matching bandwidth or multi-band response can be obtained using a single layer U-slot rectangular antenna with a probe feed. However, the determination of the input impedance of this antenna has not been reported. In this letter using segmentation analysis a new explicit matrix input impedance formula has been derived. The U-slot rectangular antenna is partitioned into rectangular segments and the system of coplanar matrix circuit equations is reduced by cojoining pairs of equations. The reduced system is then solved to obtain a new explicit matrix input impedance formula. This technique has the potential to be applied to other multi-segmented antenna geometries. Two antennas operating at 2.45 GHz were fabricated, one with a substrate of thickness 1.575 mm and the other with a substrate of thickness of 3.175 mm. For both antennas there is an excellent agreement between the predicted, simulated, and measured results for the input impedance.