This paper concerns with the construction of three distinct polynomials with integer coefficients (a1, a2, a3) such that the product of any two contribution of the set subtracted to their sum and improved by a non-zero integer (or a polynomial with integer coefficients) is a perfect square and this shows the non-extendibility of Special Dio Quadruple. Keywords: Special Dio triples, Pyramidal number, Polynomials, Pell equation, Special Dio Quadruples.