In this paper it is proved that for n≥5 there exists a constant δ(n) with 1/4<δ(n)<1 such that any weakly stable Yang-Mills connection over a simple connected compact Riemannian manifold M of dimension n with δ(n)-pinched sectional curvatures is always flat. The pinching constants are possible to compute by elementary functions. Moreover we give some remarks on stability of Yang-Mills connections over certain symmetric spaces.
