In this paper the concept of negative energy waves facilitates the analysis of instability in a magnetized bi-ion plasma with differential ion streaming. There are three frequency regimes in which instability may arise. For frequencies less than the alpha particle gyrofrequency, a negative energy alpha ion-cyclotron mode can interact with a positive energy proton-cyclotron mode. In the intermediate frequency regime lying between the alpha and proton gyrofrequencies, a negative energy alpha-acoustic mode interacts with a positive energy proton-cyclotron mode. In the high-frequency regime above the proton-cyclotron frequency a negative energy alpha-acoustic mode interacts with a positive energy proton-acoustic mode. The resonance (or coalescence) condition which lends itself to a simple geometrical interpretation as the intersection between the proton and alpha mode wave normal diagrams with differential streaming permits the evaluation of the instability growth rate in each frequency regime, which is calculated for both subsonic and supersonic differential streaming.