TCPN (timing constraint Petri nets) is an important kind of time-related Petri nets. Some basic concepts are redefined to enrich and perfect corresponding the theory of TCPN. Firstly, the rigorous definitions for weak and strong schedulability of a transition are redefined to correct the irrationality of the original ones. The verification method for the strong schedulability is presented in the form of a theorem. Secondly, the definition of schedulability of TCPN is given and the corresponding necessary and sufficient condition is proposed. Finally, the characteristic of TCPN along with Petri nets and other time-related Petri nets is analysed. It is of certain illumination and referrence, both in research of time-related Petri nets and in modeling real-time systems.