In this paper, we point out that the recent conclusion concerned with the geodesic convex hull and geodesic convex combination on Hadamard manifolds is not rigorous and explain why the conclusion does not hold like it in linear spaces. Therefore, a notion of geodesic pseudo-convex combination is proposed to show that the Knaster-Kuratowski-Mazurkiewicz (KKM) theorem still holds under some mild conditions on Hadamard manifolds.