In a recent paper, Feng et al. [5] (Two-agent scheduling with rejection on a single machine. Appl. Math. Model. 39 (2015) 1183-1193) studied some two-agent scheduling problems with rejection on a single machine. The authors showed that all problems are NP-hard and then provided four dynamic programming algorithms. Unfortunately, we observe that some mistakes are contained in the two dynamic programming algorithms. In this note, we first show by a counter-example that the above two algorithms are incorrect. Furthermore, we also provide two new dynamic programming algorithms to solve the same problems.