Consider the unnormalized Ricci flow ( g ij ) t = -2 R ij for t ∈ [0, T ), where T < ∞. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T ), then the solution can be extended beyond T . We prove that if the Ricci curvature is uniformly bounded under the flow for all times t ∈ [0, T ), then the curvature tensor has to be uniformly bounded as well.