Prediction of major disruptions occurring at the β -limit for tokamak plasmas with a normal magnetic shear in JT-60U was conducted using neural networks. Since no clear precursors are generally observed a few tens of milliseconds before the β -limit disruption, a sub-neural network is trained to output the value of the βN limit every 2 ms. The target βN limit is artificially set by the operator in the first step to train a network with non-disruptive shots as well as disruptive shots, and then in the second step the target limit is modified using the βN limit output from the trained network. The adjusted target greatly improves the consistency between the input data and the output. This training, the 'self-teaching method', has greatly reduced the false alarm rate triggered for non-disruptive shots. To improve the prediction performance further, the difference between the output βN limit and the measured βN, and 11 parameters, are inputted to the main neural network to calculate the 'stability level'. The occurrence of a major disruption is predicted when the stability level decreases to the 'alarm level'. Major disruptions at the β -limit have been predicted by the main network with a prediction success rate of 80% at 10 ms prior to the disruption while the false alarm rate is lower than 4% for non-disruptive shots. This 80% value is much higher than that obtained for a network trained with a fixed target βN limit set to be the maximum βN observed at the start of a major disruption, lower than 10%. A prediction success rate of 90% with a false alarm rate of 12% at 10 ms prior to the disruption has also been obtained. This 12% value is about half of that obtained for a network trained with a fixed target βN limit.