Characteristics of radiation of XeBr* molecules (at the B -- > X transition, lambda ~ 282 nm) under the conditions of electrodeless capacitive discharge are studied experimentally. It is shown that the high output power and efficiency of radiation of the XeBr* molecules are achieved in the pressure range from 4 to 12 mm Hg, and the maximum efficiency corresponds to the excitation power of 2-3 10-18 W per one molecule. The mean output power up to 5.5 W is achieved at the power density up to 33 mW/cm2 and the efficiency up to 15%. A sealed-off XeBr* excilamp is created.