Abstract: The Convention on the Recognition and Enforcement of Foreign Arbitral Awards of June 10, 1958 (the 1958 New York Convention) allows recognition and enforcement of arbitral awards in most countries of the world. Court practice of the states has revealed some problems of application of the 1958 New York Convention. One of such problems is recognition and enforcement of the arbitration award cancelled by the state court in the place where it was made. In the process of research of legal consequences of execution of annulled arbitral awards both general scientific methods of knowledge (analysis and synthesis, induction and deduction, generalization) and special scientific methods (formal-logical, formal-legal and method of legal prediction) were used. The scientific novelty of this work is the rationale that the recognition and enforcement of annulled arbitral awards lead to negative consequences. Enforcement of arbitral awards annulled at the place of their rendering undermines the status of such institution as arbitral dispute resolution and the whole system of acts aimed at regulating the activity of arbitration. Execution of such decisions leads to a violation of the principles of legal certainty, lis pendens, res judicata, pacta sunt servanda, and most importantly - violates the rights of participants in arbitral proceedings. It is noted that attempts are being made to amend the mechanism of recognition and enforcement of arbitral awards, established by the 1958 New York Convention, with regard to the enforcement of annulled arbitral awards. It is proposed to make such changes through the adoption of an additional protocol to the 1958 New York Convention or a new international treaty.