Operational forecasting systems often combine calibrated probabilistic outputs from several numerical weather prediction (NWP) models. A common approach is to use a weighted blend, with the more accurate models having higher weights. We show that this approach is not ideal and that using a simple neural network to combine forecasts yields better results. The sharpness of the forecast is increased, so that extreme events are more likely to be predicted. Improvements are also observed in accuracy as measured by the continuous rank probability score (CRPS) and reliability. The proposed neural network model has a simple architecture with few parameters, and training and inference can easily be done using a central processing unit. This makes it a practical option for improving the accuracy of blended operational forecasts.