In this paper, we present an ultra-wideband full-duplex antenna system constituted of a wideband 4-element Vivaldi array and wideband microstrip-to-slotline baluns. The proposed system is characterized by its simplicity, high directivity, and high self-interference cancellation levels over a wide frequency bandwidth. The system is abricated using basic PCB technology and can provide at least 50 dB of self-interference cancellation over the bandwidth of operation, 4 - 40 GHz, with an average gain of 7.8 dBi. The system has a size of 8 cm x 8 cm x 9.4 cm and can be used as a high data rate link between two distant wireless nodes. To assess the merits of the proposed system and compare it to other published works, a new figure of merit (FoMWFD) dedicated to wide-band full-duplex antenna topologies is introduced in this paper.