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A perfectly conducting bowtie antenna exhibits broadband properties. Variable resistive loading is the strategy sometimes used to minimize the reflections from the end of the bowtie antenna, but its practical implementation can be difficult and its overall efficiency very low. We continue investigation of an antenna design with a constant resistive loading (Popovic´, M. and Popovic´, B.D., Proc. URSI XXVIIth General Assembly, 2002; Randa, J. et al., IEEE Int. Symp. on Electromagnetic Compatibility, p.265-6, 1991), where the reflection-minimizing strategy by accurate loading variation is replaced by a favorable change in the antenna geometry. We report results. of FDTD analysis for an "inverted bowtie" antenna geometry. The antenna is wide at its apex, and its width is tapered along the longitudinal axis towards its ends. With a constant surface resistivity, therefore, the resistance per unit length increases along the longitudinal direction. The gradient of resistance per unit length can be controlled by careful design of the taper. The authors nicknamed the design as the "Dark Eyes" antenna, as the geometry is reminiscent of the eye shape. The FDTD simulations demonstrate that broadband antenna behavior in the range of 4 to 8 GHz is improved for lower values of surface resistive loading.