The criterion Vd/VAe)1/2 for instability mentioned in the existing theories is based on the assumption βi《 1. The present study investigates the effects of finite βe and βi on the ion-ion streaming instability. It is found that within the domains under investigation in the parameter space the growth rate increases with the increase of βe. Moreover, the unstable region, as a function of the streaming velocity Vd/VA, becomes broader. On the other hand, when βi increases (for a given βe) the unstable region in the Vd/VA space becomes narrower.