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We propose the realization of Majorana fermions (MFs) on the edges of a two-dimensional topological insulator in the proximity with s-wave superconductors and in the presence of transverse exchange field h.It is shown that there appear a pair of MFs localized at two junctions and that a reverse in the direction of h can lead to permutation of two MFs.With decreasing h,the MF states can either be fused or form one Dirac fermion on the π-junctions,exhibiting a topological phase transition.This characteristic can be used to detect physical states of MFs when they are transformed into Dirac fermions localized on the π-junction.A condition of decoupling two MFs is also given.