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A test for determining the zero distribution of a real polynomial with respect to the imaginary axis is presented. It is based on the construction of a sequence of polynomials of descending degree which draws on the Levinson algorithm. The proof of the stability criterion, which is based on intuitive geometrical considerations, is very simple, and the computational complexity is not greater than that for the Routh test. The critical situations that may arise are also examined and some examples are given.