The well-posedness of hyperbolic initial boundary value problems is linked to the occurrence of zeros of the so-called Lopatinskii determinant. For an important class of problems, the Lopatinskii determinant vanishes in the hyperbolic region of the frequency domain and nowhere else. In this paper, we give a criterion that ensures that the hyperbolic region coincides with the projection of the forward cone. We give some examples of strictly hyperbolic operators that show that our criterion is sharp.