Summary: As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of three-body operators of the form \(\delta_{1\alpha} \delta_{2\beta} \delta_{3\gamma}\), the construction of entangled states for a three-particle system is investigated. It is shown that there exist 54 different sets of operators (each containing four commuting three-body operators with their product being \(-1\)) and any three members of each set constitute a CSCO. It is found that 54 different sets of maximally entangled states can be constructed, including the usual GHZ (Greenberg–Horne–Zeilinger) state as a special case. Once a preferential representation is adopted, all of them can be expressed as a GHZ-like form. Moreover, there also exist 18 sets of partially entangled states, where only two particles are entangled.