For any positive integers k≥3 and λ, let cd(k,λ) denote the smallest integer such that the necessary conditions 2λ(v−1)≡0 (mod k−1) and λv(v−1)≡0 (mod (k2)) for the existence of a DB (k,λ;v) are also su3cient for every v≥cd (k,λ). Inthis article we provide anestimate for cd(k,λ) when k≡0 (mod 4) and any λ. Combined with the results in (Discrete Math. 222 (2000) 27-40), we completely give anestimate of cd(k,λ) for any integers k≥3 and λ.