This paper describes the single-electron detachment process of a negative hydrogen ion in collisions with a helium atom. There are two electrons with different ionization potentials in the negative hydrogen ion in the ground state. We consider the detachment processes of these two electrons in the negative hydrogen ion and the corresponding detached electron wavefunctions, which depend on the initial binding energies of each electron. We treat these processes separately. We then calculate the electron detachment cross sections from the negative hydrogen ion accompanying the formation of not only the ground state, but also the excited state of the neutral hydrogen atom in the exit channel. The results show that the contribution of the excited states formed in the electron detachment processes, which has been neglected so far, is important in the high-energy region. The calculated results of the total and partial single-electron detachment cross section from the negative hydrogen ion are found to be in good agreement with the experimental data obtained so far.