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=p^k, r=2p^k, r²+1=p and r²+1=2p^k for an odd prime p and a positive integer k, the D(−1)-pair {1, r²+1} cannot be extended to a D(−1)quadruple.