A (v, K, λ) difference family ((v, K, λ)-DF in short) can be used to construct a (v, K, λ)-PBD. A lot of work has been done on the existence of (v, k, 1) difference families ((v, k, 1)-DF in short) when K = {k} is a singleton. For K = {3, 4}, partial results have been obtained by Buratti. In this paper, it is proved that there exists a balanced (q, {3, 4}, 1)-DF for each prime power q ≡ 1 (mod 18)