This study discusses the subject of training data selection for neural networks using back propagation. We have made only one assumption that there are no overlapping of training data belonging to different classes, in other words the training data is linearly/semi-linearly separable . Training data is analyzed and the data that affect the learning process are selected based on the idea of Critical points. The proposed method is applied to a classification problem where the task is to recognize the characters A,C and B,D. The experimental results show that in case of batch mode the proposed method takes almost 1/7 of real and 1/10 of user training time required for conventional method. On the other hand in case of online mode the proposed method takes 1/3 of training epochs, 1/9 of real and 1/20 of user and 1/3 system time required for the conventional method. The classification rate of training and testing data are the same as it is with the conventional method.