We examine the properties of edge states in a two-dimensional topological insulator. Based on the Kane-Mele model, we derive two coupled equations for the energy and the effective width of edge states at a given momentum in a semi-infinite honeycomb lattice with a zigzag boundary. It is revealed that, in a one-dimensional Brillouin zone, the edge states merge into the continuous bands of the bulk states through a bifurcation of the edge-state width. We discuss the implications of the results to the experiments in monolayer or thin films of topological insulators.PACS numbers: 73.20. At,71.70.Ej,72.25.Dc Topological insulators (TI) are one of the fascinating fields which have attracted extensive studies in condensed matter physics for the past decade [1,2]. This phenomenon can be traced back to quantum Hall effect (QHE) in two-dimensional (2D) systems under high magnetic fields. The QHE is characterized by the presence of gapless edge states with a finite gap in the bulk. This metallic edge channel is revived in TI with timereversal symmetry (TRS) preserved. This edge state is also known to be topologically protected as in the QHE.The study of TI was first initiated theoretically in 2D systems [3,4] dubbed as a quantum spin Hall effect, where spin-orbit coupling(SOC) plays an important role [5][6][7][8]. It was subsequently generalized to the TI in 3D systems with a single Dirac-cone dispersion on the surface [9][10][11]. Finally, the TI state in 2D systems has been confirmed experimentally by transport measurements in HgTe/CdTe quantum well [12,13] . In spite of some improvements, the reduction of the bulk carrier density is not sufficient to suppress completely the bulk contribution of the transport due to the difficulty of the fine tuning of the doping concentration. An alternative way to control the bulk carrier density is to reduce the sample size or to apply gate voltage. Epitaxially grown thin films of Bi 2 Se 3 showed weak antilocalization effects with large magnetic field, which represents the surface state of TI.[21] Nonetheless, the reduction in the sample size inevitably induces a gap in the metallic dispersion of TI due to the overlap of the surface states at the two opposite surfaces [22,23], which requires a detailed study of the surface or edge states. In 2D TI, some existing works have been performed on the properties of edge states [13,24]. However, general understanding of the spatial features of the edge state is still lacking. Particularly, we need systematic researches on the dependence of the spatial features of the edge states on various physical parameters, which is a main motivation of this work.In this Letter, we investigate theoretically the spatial variation of the edge states in the 2D TI. Many theoretical models have been proposed for the understanding of TI, with the increasing demands on its research. KaneMele (KM) model [3,25] is one of the prototype model of 2D TI. This model shows a bulk energy gap on the honeycomb lattice due to the SOC, but its edge states on the boundarie...