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Rigorous full-wave analysis of a slot-coupled hemispherical dielectric resonator (DR) antenna has been recently reported. This kind of slot-coupled DR antenna has the advantage of mechanical simplicity and avoids large probe self-reactances, as compared to a probe-fed DR antenna. In this paper, we extend the study of a hemispherical shape to a multilayered hemispherical configuration. The geometry of a two-layered hemispherical DR antenna with slot coupling is shown, where the permittivity of the outer-layer dielectric is chosen to be about half that of the inner-layer dielectric. In this case, the outer-layer dielectric can serve as a transition region between the air and the inner-layer dielectric, and thus can increase the bandwidth of the antenna. To accurately determine the antenna bandwidth, the input impedance of the slot-coupled DR antenna is derived using the reciprocity theorem and a Green's-function formulation. Numerical results are then calculated using a moment-method calculation.