Development of the steady-state potential in a two-electron-temperature plasma in contact with the wall is investigated analytically. It is shown that if the hot- to cold-electron temperature ratio is of the order of 10, the potential drop in the presheath is allowed to have either a small value characterized by the cold electrons or a large value by the hot electrons, and discontinuously changes at a critical value for the hot- to total-electron density ratio. It is also found that the monotonically decreasing potential structure, which consists of the first presheath, a current-free double layer, the second presheath, and the sheath, can be steadily formed in a lower range of the hot- to total-electron density ratio around the critical value. The current-free double layer is set up due to existence of the two electron species and cold ions generated by ionization so as to connect two presheath potentials at different levels.