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The energy dependence of multiplicity fluctuations was studied for the most central Pb+Pb collisions at 20A, 30A, 40A, 80A and 158A GeV by the NA49 experiment at the CERN SPS. The multiplicity distribution for negatively and positively charged hadrons is significantly narrower than Poisson one for all energies. No significant structure in energy dependence of the scaled variance of multiplicity fluctuations is observed. The measured scaled variance is lower than the one predicted by the grand-canonical formulation of the hadron-resonance gas model. The results for scaled variance are in approximate agreement with the string-hadronic model UrQMD.