This is a randomized, multi-center, parallel-group, active-controlled, double-blind study evaluating the effects of mometasone furoate (MF) dry powder inhaler (DPI) on bone mineral density (BMD) in subjects with asthma. The mean percent change in lumbar spine BMD from the averaged baseline value (the average of the two scan results prior to treatment) to the endpoint of treatment time point (the average of the last two valid post-baseline scan results during treatment) for the comparison of MF DPI 400 mcg daily in the evening versus montelukast (ML) 10 mg daily in the evening.