The modern methods for power system load prediction are usually based on Artificial Neural Networks (ANN), which present satisfactory results. However, the estimation of the confidence intervals can not be applied directly, unlike to the classical forecasting methods. One of the most commonly used methods is the re-sampling technique, which calculates the respective confidence interval based on the training data set. The limits of the training set confidence interval are also applied in the case of the real prediction giving satisfactory but slightly underestimated results. The targets of this paper are: (1) to apply the basic re-sampling method for the short term forecasting of the next day load in the interconnected Greek power system using an optimized ANN proving the aforementioned disadvantage and (2) to propose a modified re-sampling technique using a proper corrective multiplication factor. Finally, the next day load demand of the test set is estimated using the best ANN structure and the modified confidence intervals.