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LLM-based assistants, such as GitHub Copilot and ChatGPT, have the potential to generate code that fulfills a programming task described in a natural language description, referred to as a prompt. The widespread accessibility of these assistants enables users with diverse backgrounds to generate code and integrate it into software projects. However, studies show that code generated by LLMs is prone to bugs and may miss various corner cases in task specifications. Presenting such buggy code to users can impact their reliability and trust in LLM-based assistants. Moreover, significant efforts are required by the user to detect and repair any bug present in the code, especially if no test cases are available. In this study, we propose a self-refinement method aimed at improving the reliability of code generated by LLMs by minimizing the number of bugs before execution, without human intervention, and in the absence of test cases. Our approach is based on targeted Verification Questions (VQs) to identify potential bugs within the initial code. These VQs target various nodes within the Abstract Syntax Tree (AST) of the initial code, which have the potential to trigger specific types of bug patterns commonly found in LLM-generated code. Finally, our method attempts to repair these potential bugs by re-prompting the LLM with the targeted VQs and the initial code. Our evaluation, based on programming tasks in the CoderEval dataset, demonstrates that our proposed method outperforms state-of-the-art methods by decreasing the number of targeted errors in the code between 21% to 62% and improving the number of executable code instances to 13%.