The two-stream instability is common, responsible for many observed phenomena in nature, especially the interaction of jets of various origins with the background plasma (e.g. extragalactic jet interacting with the cosmic background). The dispersion relation that does not consider magnetic fields is described by the well-known Buneman relation. In 2011, Bohata, Břeň and Kulhánek derived the relation for the two-stream instability without the cold limit, with the general orientation of a magnetic field, and arbitrary stream directions. The maximum value of the imaginary part of the individual dispersion branches wn(k) is of interest from a physical point of view. It represents the instability growth rate which is responsible for the onset of turbulence mode and subsequent reconnection on the scale of the ion radius accompanied by a strong plasma thermalization. The paper presented here is focused on the non-relativistic instability growth rate and its dependence on various input parameters, such as magnitude and direction of magnetic field, sound velocity, plasma frequency of the jet and direction of the wave vector during the jet — intergalactic medium interaction. The results are presented in plots and can be used for determination of the plasma parameter values close to which the strong energy transfer and thermalization between the jet and the background plasma occur.