Murat took part at the 2000 Korean Open Tournament in Chuncheon, at which she won the gold medal in the juniors category and was named "Most Technical Junior Woman Athlete". She took a gold medal at the 2000 World Cup in Lyon, France. In 2004, she became the European champion in Lillehammer, Norway. She won the silver medal at the 2005 World Taekwondo Championships in Madrid, Spain. The same year, she won another silver medal at the European Championships held in Riga, Latvia.