In this article, the author analyses the question whether it is possible for the arbitrators, after their original award had been annulled, to sit on the arbitration tribunal hearing the case again, to reconsider the case, and to issue a second award in the same case in light of the UNCITRAL Model Law regulations. This question is addressed from two basic perspectives. The first one relates to arguments rooted in the functus officio principle, especially in reference to rectification and remission proceedings, as laid down in relevant regulations. The second perspective, meanwhile, encompasses the ethical principles and usages concerning appointment of arbitrators in international commercial arbitration, including the concept of prejudgment. In her conclusions, the author rejects a blanket prohibition on re-appointment of arbitrators, arguing that it does not duly account for all the nuances of the notion of impartiality in the context of actual practice.