In this paper, we show that some parametric families of D(-- 1)-triples cannot be extended to D(-- 1)-quadruples. Using this result, we further show that in each case of r = pk, r = 2pk, r2 + 1 = p and r2 + 1 =2pk for an odd prime p and a positive integer k, the D(-l)-pair {1, r2 + 1} cannot be extended to a D(-- l)quadruple.