The notion of branching bisimulation with explicit divergence was introduced by van Glabbeek and Weijland.It is used to define an equivalence relation ≈_b^△,which means to be the weakest equivalence with the property of branching bisimulation and divergence preservation.However,in that paper it only claims that ≈_b^△ is an equivalence with such properties without proofs,and as it turns out that the proving is not obvious.In this paper we introduce an equivalence relation called coloured complete trace equivalence,and prove that it is the weakest equivalence which has the property of branching bisimulation equivalence and is also divergence preserving.We then prove that the coloured complete trace equivalence coincides with ≈_b^△,thus supplementing the work of van Glabbeek and Weijland.