He was re-elected during the 21st plenary of the ICTR held in Arusha on Friday.
The plenary also approved judge Khalid Rachid Khan from Pakistan to continue as ICTR Vice-President for another two-year term.
Justice Byron joined ICTR in June 2004. Prior to his assignment at the UN Court, he served as the Chief Justice of Eastern Caribbean Supreme Court.
He began his career in private practice as a Barrister in 1966.
In 2000, judge Byron was conferred the honour of Knight Bachelor by Her Majesty Queen Elizabeth II.
Judge Khan joined ICTR in August 2003. Before that, she served as judge of the High Court of Peshawar, where she was first Pakistani woman ever appointed to the position.
She began her career as a civil judge in 1974 and later became the Deputy Secretary in Law Department of the government o North-West Frontier Province.
The ICTR was established by UN Security Council in November, 1994 to try key suspects of Rwanda genocide, which claimed lives of about 800,000 people, mostly ethnic Tutsis and moderate Hutus.
The Tribunal has so far convicted 38 persons and acquitted six.
© Hirondelle News Agency