This paper assesses the role of concentrated bank borrowing in explaining the extensive and intensive margins of export, while accounting for the simultaneous relationship between exporting and innovation. Concentrated bank borrowing proxies for the intensity of the bank–firm relationship and is a strategy often pursued by small and medium enterprises (SMEs) in order to overcome information asymmetries and improve access to external finance. Our results show that a tight relationship between an SME and its main bank increases both the firm's probability of exporting and its export intensity. This positive effect is only marginally mediated by the SME's increased propensity to introduce product innovation. We further discuss the financial and non‐financial channels through which the intensity of the bank–firm relationship supports SMEs’ international activities.