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The following theorem is know as Nielsen's Theorem on finite mapping classes: if M is a closed orientable surfaces and if H : M → M is a map whose n-th power homotopic to the identify, then H is homotopic to a homeomorphism K with Kⁿ = identity. In this work we show that Nielsen's Theorem fails in dimension bigger than two. In other words for each integer m ≥ 3 we construct a m-dimensional closed orientable manifold M together with a homeomorphism H : M → M, such that the n-iterated of H is homotopic to the identity but H itself is not homotopic to a homeomorphism K : M → M satisfying Kⁿ = I_M.