A binding hot spot is a small area at a protein-protein interface that can make significant contribution to binding free energy. This work investigates the substantial contribution made by some special co-occurring atomic contacts at a binding hot spot. A co-occurring atomic contact is a pair of atomic contacts that are close to each other with no more than three covalent-bond steps. We found that two kinds of co-occurring atomic contacts can play an important part in the accurate prediction of binding hot spot residues. One is the co-occurrence of two nearby hydrogen bonds. For example, mutations of any residue in a hydrogen bond network consisting of multiple co-occurring hydrogen bonds could disrupt the interaction considerably. The other kind of co-occurring atomic contact is the co-occurrence of a hydrophobic carbon contact and a contact between a hydrophobic carbon atom and a pi ring. In fact, this co-occurrence signifies the collective effect of hydrophobic contacts. We also found that the B-factor measurements of several specific groups of amino acids are useful for the prediction of hot spots. Taking the B-factor, individual atomic contacts and the co-occurring contacts as features, we developed a new prediction method and thoroughly assessed its performance via cross-validation and independent dataset test. The results show that our method achieves higher prediction performance than well-known methods such as Robetta, FoldX and Hotpoint. We conclude that these contact descriptors, in particular the novel co-occurring atomic contacts, can be used to facilitate accurate and interpretable characterization of protein binding hot spots.