This research discusses one of the most important means of reducing corruption in public sector companies and government departments, a relationship of cooperation and coordination between the external auditor and internal auditor, in the light of ISA (610), the recommendations of the International Organization of Supreme Audit Institutions (INTOSAI) and the National Strategy to combat corruption. The research was based on two assumptions: the first was weak relationship of cooperation and coordination between the external auditor and internal auditor leads to weakness of measures to curb and reduce the administrative and financial corruption, and the second weakness of the administration's awareness of the importance of this cooperation and coordination leads to the weakness of the measures to curb corruption .The researcher dealt with the research problem of the weakness in the relationship between external auditors and internal auditors and the weakness of the independence of the internal auditor in the public sector units and government departments, and inadequate legislation and auditing standards local to determine the nature of their relationship The research found a set of conclusions and recommendations, and the main conclusions was the agreement about the answers of the research sample from (auditors and internal auditors and general managers of public sector units and government departments) on the need for cooperation and coordination between the external auditor and internal auditor. The most important methods of cooperation and coordination is to hold joint meetings to the challenge the common goals and joint planning (the exchange control reporting between them. While the most prominent recommendations were issue a standard audit local specifies the modalities of cooperation and coordination received in the recommendations of the International Organization of Supreme Audit, Finance and Accounting (INTOSAI), which was agreed by the research sample as well as the need for professional organizations in Iraq represented by the Association Accountants and the Council of the profession of audit and account auditing of spreading the culture of cooperation and coordination between external auditor and internal auditor, as well as the addition of legal materials in the Companies Act (No. 21) and (22) for the year 1997 (amending) a clear definition of the nature of their relationship.