The cost-effectiveness of operations on the Web enables financial service firms to employ Web technology to replace or substantially reduce the need for personal interactions in the provision of their services. However, recent cases have shown that the use of Web technology in financial services may not be as promising as expected. This study utilises the constructs derived from transaction cost analysis (TCA), the technology acceptance model (TAM) and relationship marketing literature to develop a framework of the antecedents to using Internet banking. The model explicitly incorporates the impact of the experiences a customer has had with services provided by the physical bank whose Web services the customer is considering using. The results show that the major antecedent variables in TAM and the customers’ specific assets already invested in the focal physical bank have a significant impact on customers’ attitude towards the use and the intention to use a bank's Internet banking services. Our findings suggest that beyond the ease of use and usefulness of information system, companies have to take advantage of customer relationship built up in the offline environment that has the potential to influence customers’ use intention towards Internet service. The study advances the technology acceptance literature in terms of explaining users’ new-service-adoption behaviour by adding the concepts from TCA and customer relationship literature.