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Coulomb implosion mechanism of the negatively charged ion acceleration in laser plasmas is proposed. When a cluster target is irradiated by an intense laser pulse and the Coulomb explosion of positively charged ions occurs, the negative ions are accelerated inward. The maximum energy of negative ions is several times lower than that of positive ions. The theoretical description and Particle-in-Cell simulation of the Coulomb implosion mechanism and the evidence of the negative ion acceleration in the experiments on the high intensity laser pulse interaction with the cluster targets are presented.