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An accurate prediction of stock market index is important for investors to reduce financial risk. Although quite a number of deep learning methods have been developed for the stock prediction, some fundamental problems, such as weak generalization ability and overfitting in training, need to be solved. In this paper, a new deep learning model named Random Long Short-Term Memory (RLSTM) is proposed to get a better predicting result. RLSTM includes prediction module, prevention module, and three full connection layers. Input of the predi