Primary Objective: To test the hypothesis that 6 months treatment with glatiramer acetate (GA) decreases epileptiform activity in young girls with Rett syndrome. Primary Safety Objective:To evaluate the safety and tolerability of 6 months treatment with GA in these patients. Secondary Objectives: 1. To test the hypothesis that 6 months treatment with glatiramer acetate (GA) improves respiratory dysfunction. 2. To evaluate the effect of GA treatment on general behaviour communication, hand stereotyping, feeding, sleep and other autonomic symptoms: gastrointestinal and cardiac. 3. To assess the effect of GA treatment on bodily development. Primary Endpoint:Improvement of epileptiform activity as recorded in a 24-hours EEG. Primary Safety Endpoint:Frequency and severity of treatment-related AEs (including safety lab parameters). Secondary Endpoints: 1. Improvement in the scoring of breath holds and hyperventilation, as measured with non-invasive respiratory inductance plethysmography (NoxT3 device) and parents' diaries. 2. Changes in general behaviour, communication, feeding and motor skills as assessed by the investigator (based on Kerr and Naidu validated severity scores) and recorded in parents' diary. 3. Decrease in seizure frequency as reported in parents' diary. 4. Improvement in sleep schedule as recorded in a sleep diary. 5. Change in height and weight. Population:Ten girls, 6 to 15 years old, diagnosed with Rett syndrome (RTT) Study Design:This is a single - center, exploratory, open-label, study in 10 girls diagnosed with RTT. The study will consist of four parts: Screening and baseline assessments, initial and final dose-setting period, treatment period and end-of study follow-up. Investigational Product:Glatiramer Acetate (Copaxone® , Teva Pharmaceutical Industries Ltd.) Sample Size Consideration: The planned sample size of 10 patients was considered adequate by the investigator for this phase I exploratory proof-of-concept study. The study is not expected to show statistical significance or statistical power, only a trend for the study endpoints. Each patient will serve as her own control. Duration of Study: Approximately 8 months per patient (including up to 2 weeks pre-treatment assessment, 6 months initial dose and treatment periods and end-of study visit). Overall study duration: the study is expected to be completed within 12 months (dependent on rate of recruitment).