The efficient siphon computation is the key to the development of siphon-based deadlock control strategies with good performance. This work studies the computation of minimal siphons in a class of Petri nets called S⁴PR. Firstly, we propose a function with polynomial complexity to determine whether a resource subset can generate a minimal siphon. Next, using the technique of problem partitioning, a new approach is developed to compute all minimal siphons in S⁴PR. Finally, an example is given to illustrate the proposed approach.