We have investigated in detail the quasibound states of a quantum channel with a multiple double-bend discontinuity. We assume that our quantum system is of finite length and connected to two 2DEG reservoirs. The mode-matching technique has been employed. We have predicted that there are 2N resonant peaks of the conductance below the first transverse-mode energy for the quantum channel with an N double-bend discontinuity, which means the formation of one-electron miniband structure below the first transverse-mode energy for a lateral superlattice consisting of finite periods of double-bend structure. Our results clearly indicate that the 2N quasibound states of the channel with energies below the first transverse-mode energy are 2N-fold splitting quasibound states due to the coupling between the local bound states. Our analytical results from the nearest interactive model and our numerical results are qualitatively well consistent.