  We propose to realize Majorana fermions (MFs) on an edge 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 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 {\pi}-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
{\pi}-junction. A condition of decoupling two MFs is also given.
