  We consider solitary water waves on the vorticity flow in a two-dimensional
channel of finite depth. The main object of study is a branch of solitary waves
starting from a laminar flow and then approaching an extreme wave. We prove
that there always exists a bifurcation point on such branches. Moreover, the
crossing number of the first bifurcation point is 1, i.e. the bifurcation
occurs at a simple eigenvalue.
