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It has been theoretically established that shear plasma flows at the boundary of the medium can generate eight MHD modes, of which only one can be unstable due to the development of the Kelvin-Helmholtz instability. It is shown that oblique perturbations propagating at an angle with respect to the velocity vector play a dominant role in the development of this instability. Analytic expressions are obtained for the criteria and instability increments that take into account the angle of propagation of perturbations, the effect of the magnetic field, and the compressibility of the medium and in the limiting cases coincide with the previously obtained results. It is noted that the appearance of a large number of waves can lead to a flow with a complicated structure at the boundary of the magnetotail.