This article presents a new four-port electronic device - the directional quadrature hybrid isolator (DQHI). The topology of this duplexer is similar to the four-arm quadrature hybrid (QH) except for a 90° non-reciprocal phase shifter (NRPS) replacing one of the λ/4 Z0 arms. We derive the DQHI S-parameters and show that it performs a 0°/90° power division for an incident signal at port 2 into ports 3 and 4 exactly like a QH, functions as an ideal isolator between ports 1 and 2, enables high-isolation between port 1 to ports 3 and 4 and facilitates injection of self-interference cancellation (SIC) signal from port 4 into 3. Analytic evaluation of a dual-port N-path circuit as an NRPS is performed and the theoretical impact on the DQHI performance is examined. An 8-path, 65-nm NMOS design is utilized to simulate the performance with a 1 GHz clock resulting in 1.7 dB TX-to-antenna loss, antenna-RX loss of 3 dB, SIC-to-RX loss of 6.6 dB, TX-RX and TX-SIC isolations of 26 and 12.5 dB respectively.