Let p, q be distinct odd primes, and let a, b be positive integers. In this paper we prove that if S(pa, qb) is a Storer difference set with the parameters ν = paqb, k = (ν−1)/4 and λ =(ν−5)/16, then we have a = b = 1, p =(ρ3r+ρ−3r−1)/3 and q = ρ3r+ρ−3r+1, where ρ = 2+√3, ρ− = 2 − √3, and r is a positive integer.