This paper presents a detailed analysis of the Buneman-Farley two-stream plasma instability. We use a fluid plasma model appropriate for the E region ionosphere, including the effects of the geomagnetic field and electron and ion temperatures and their collisions with neutrals. We derive a linearized dispersion equation for the coupled electron thermal wave and ion thermal wave. The results are compared with those derived from a kinetic theory. It is shown that in the long-wavelength limit the agreement between the above described fluid theory and kinetic theory is exact. The physical arguments for the agreement are clearly stated. From the dispersion equation we obtain closed form expressions for the phase velocities, frequencies, and growth rates describing the threshold condition and the unstable region. With these closed form results we are able to determine the physical behavior of the instability under a variety of ionospheric conditions. The closed form results show that unstable plasma waves having the maximum growth rate propagate at finite off-perpendicular angles with respect to the geomagnetic field. This property, together with the fact that the two-stream instability is a convective instability, is used to infer that radar auroral echoes scattered from these waves should occur at finite off-perpendicular angles. Spatial maps of radar auroral echoes obtained with a 1210-MHz backscatter radar at Homer, Alaska, are presented as supporting evidence. By taking data during magnetic conditions, we were able to exclude magnetic field line distortion as a possible contributing factor.