In this paper we prove that there exist 4-{v; k, k, k, k; λ} supplementary difference sets (SDSs) with v = q2, q ≡ 1 (mod 4) a prime power, k = q(q - 1) 2, λ = 4k - v, and Williamson matrices of order 4tv for t ε{lunate} S = {2k + 1:0 ≤ k ≤ 16} ∪ {37, 59, 61, 67 } ∪ {2i · 10j...