The problem of finding geodesics that avoid certain obstacles in negatively curved manifolds has been studied in different situations. In this note we give a generalization of the unclouding theorem of J. Parkkonen and F. Paulin: there is a constant s0=1.534 such that for any Hadamard manifold M with curvature ≤−1 and for any family of disjoint balls or horoballs {Ca}a∈A and for any point p∈M−⋃ a∈ACa if we shrink these balls uniformly by s0 one can always find a geodesic ray emanating from p that avoids the shrunk balls. It will be shown that in the theorem above one can replace the balls by arbitrary convex sets.