In this paper, we consider an interval polynomial p(s,k). The celebrated Theorem of Kharitonov states that p(s,k) is Hurwitz if and only if four specific vertex polynomials are Hurwitz. We now turn our attention to the design counterpart of this result and pose the following question: Is the interval polynomial completely unstable or there exists at least one Hurwitz polynomial in the family p(s,k)? If the answer to this question is affirmative, then the objective is to find such a Hurwitz polynomial.