  In this paper, we introduce an \alpha -flow for the Yang-Mills functional in
vector bundles over four dimensional Riemannian manifolds, and establish global
existence of a unique smooth solution to the \alpha -flow with smooth initial
value. We prove that the limit of solutions of the \alpha -flow as \alpha\to 1
is a weak solution to the Yang-Mills flow. By an application of the \alpha
-flow, we then follow the idea of Sacks and Uhlenbeck to prove some existence
results for Yang-Mills connections and improve the minimizing result of the
Yang-Mills functional of Sedlacek.
