Newborn babies have seizures much more frequently than either children or adults, and their seizures are often associated with serious long-term consequences such as epilepsy, learning disabilities and cerebral palsy. Although newborn seizures are very common, medications currently used to treat them are relatively ineffective and may have serious side effects. A medication called bumetanide shows great promise for treating newborn seizures because the drug blocks special channels present only in the brain cells of newborns. We will conduct a pilot trial to determine whether bumetanide is a safe drug for the treatment of newborn seizures.