A fully connected Artificial Neural Network (ANN) contains many connections. Compared to the pruned ANN with fewer connections, the fully connected ANN takes longer time to produce solutions end may not provide appropriate solutions to new unseen date. Therefore, by reducing the sloe of ANN, we can overcome the overfitting problem and increase the computing speed. In this research, we reduced the size of ANN by destroying the connections. In other words, we investigated the performance change of the reduced ANN by systematically destroying the connections. Then we found the acceptable level of connection-destruction on which the resulting ANN Performs as well as the original fully connected ANN. In the previous researches on the sloe reduction of ANN, the reduced ANN had to be retrained every time some connections were eliminated. Therefore, It tool lolly time to obtain the reduced ANN. In this research, however, we provide the acceptable level of connection-destruction according to the size of the fully connected ANN. Therefore, by applying the acceptable level of connection-destruction to the fully connected ANN without any retraining, the reduced ANN can be obtained efficiently.