This extension study will enroll individuals who have completed treatment in the parent protocol "Effect of Teriparatide, Vibration and the Combination on Bone Mass and Bone Architecture in Chronic Spinal Cord Injury" or in the teriparatide extension protocol. This study will allow those individuals who previously received teriparatide to be treated for a year with alendronate to maintain any bone they may have gained and to possibly increase bone mass further. Termination of teriparatide is followed by bone loss if anti-resorptive therapy is not initiated, so this approach is optimal for continued treatment of the current group of participants.