The main aim of this study is to provide empirical evidence examining how outsourced internal audit function (IAF) providers are associated with audit efficiency, and how such providers interact with high‐quality external auditors. We use a sample of 711 observations for companies listed on the Muscat Security Market during the period 2005–2014. Based on pooled regression, we find that audit efficiency is significantly improved when the IAF provider is from a Big4 audit firm, whereas a non‐Big4 audit firm IAF provider is associated with reduced audit efficiency. Furthermore, we find evidence suggesting significant interaction between the external auditor and IAF in relation to audit efficiency if the outsourced IAF provider is from a Big4 audit firm. In additional analysis, we construct a new measure for audit efficiency, dividing the IAF providers into Big4, second tier, and other non‐Big4, and consider the time of connection between such providers and their clients. We still observe that Big4, as an outsourced IAF provider, is more significantly associated with audit efficiency than other types of IAF provider. This paper is important because there is currently little evidence concerning the type of outsourced IAF provider; it contains useful information for auditors, companies, and regulators.