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This paper discusses the first eigenvalue on a compact Riemann manifold with the negative lower bound Ricci curvature. Let M be a compact Riemann manifold with the Ricci curvature≥ -R, R = const. ≥ 0 and d is the diameter of M. Our main result is that the first eigenvalue λ1 of M satisfies λ1 ≥π2/d2 - 0.518R.