Weakness of the arm and hand results in long-term disability for many persons who suffer a stroke. After the initial recovery phase, only limited gains are achieved by retraining the weak limb to perform daily tasks. However, new treatment strategies such as repetitive transcranial magnetic stimulation (rTMS) show promise for enhancing motor recovery after stroke. rTMS is a noninvasive technique for modifying brain activity that aims to improve motor function by correcting abnormal patterns that occur after stroke. We believe that giving rTMS right before a therapy session will prepare the brain so that the patient is better able to participate in and benefit from training of the hand and arm. The goal of this study is to test how well this new strategy works to improve recovery in people who have mild to moderate weakness of the arm and hand after stroke. Participants will receive magnetic stimulation of the movement area of the brain just prior to arm and hand training for a series of eight sessions. We will evaluate changes in hand and arm function after the intervention and one month later to see if the changes are maintained. We will also test whether some groups of people benefit more than others from the intervention. If improvements in hand and arm function are observed after the intervention, we will test it more rigourously in a future clinical trial in which participants are randomly assigned to different treatment conditions. This research will show whether brain stimulation can be used to improve the effectiveness of rehabilitation care.