Researches on trust have attracted more and more attentions in multi-agent systems and networks. However, subjective trust generally has no transitivity, which brings much non-determination on delegation, network information propagation, and the construction of subjective trust network. To this end, the paper discusses the binary value of trust relation, and its transitivity in cooperative environment. First, the study gives the definition of objective trust and subjective trust. Next, the paper proposes some useful properties of trust related to the transitivity of trust and demonstrates that objective trust has a relation of equivalence, and subjective trust has a relation of constrained symmetry and transitivity. Finally, a feasible algorithm of subjective trust closure and test algorithms for connectedness are given, and the study has demonstrated that the computational complexities of the above algorithms are polynomial order. The paper made some initial explores on transitivity of subjective trust and gives some useful basic conclusions.