In this paper, by a new constructive method, the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate characteristics. It is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise C-1 functions. In particular, the authors give the optimal control time of the system. Finally, a new example belonging to this kind of system is also provided.