In this study, people who have had a successful heart transplant will receive either active alendronate and a "dummy pill" instead of calcitriol, or active calcitriol and a dummy pill instead of alendronate for the first year after their transplant, starting within 1 month after transplant surgery. We will measure bone density in the hip and spine at the start of the study and after 6 and 12 months, and will also check for broken bones in the spine. This research should lead to ways of preventing this crippling form of osteoporosis.