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We report the relaxation dynamics from above-barrier exciton states to the lowest one in multi-stacked quantum dots (QDs). The photoluminescence decay time increases because of the excitation of higher exciton states, which is attributed to the wider miniband width of above-barrier excitons and the localization of the envelope functions in the barrier layers. The existence of the above barrier minibands makes carrier transport along the growth direction possible and eliminates a difficulty with close QD stacking. These results demonstrate an effective approach to achieve high efficiency QD devices.