A bull-design of order n is a decomposition of the complete graph Kn into bulls. Such systems exist precisely when n ≡ 0,1 (mod 5). The necessary conditions of the existence of bull-designs of λKn are the follows: λ ≡ 0 (mod 5) and n ≡ 0,1 (mod 5), or λ ≡ 0 (mod 5) and for all n. In this paper we showed the necessary conditions are also sufficient, and gave the minimum leave of the packing of the complete graph Kn.
