Drug co-prescription (or drug combination) is a therapeutic strategy widely used as it may improve efficacy and reduce side-effect (SE). Since it is impractical to screen all possible drug combinations for every indication, computational methods have been developed to predict new combinations. In this study, we describe a novel approach that utilizes clinical SEs from post-marketing surveillance and the drug label to predict 1,508 novel drug-drug combinations. It outperforms other prediction methods, achieving an AUC of 0.92 compared to an AUC of 0.69 in a previous method, on a much larger drug combination set (245 drug combinations in our dataset compared to 75 in previous work.). We further found from the feature selection that three FDA black-box warned serious SEs, namely pneumonia, haemorrhage rectum, and retinal bleeding, contributed mostly to the predictions and a model only using these three SEs can achieve an average area under curve (AUC) at 0.80 and accuracy at 0.91, potentially with its simplicity being recognized as a practical rule-of-three in drug co-prescription or making fixed-dose drug combination. We also demonstrate this performance is less likely to be influenced by confounding factors such as biased disease indications or chemical structures.