Abstract Purpose Training is an important element of human resource management (HRM) at co-operative financial institutions (CFIs), affecting their performance and their implementation of co-operative principles. Nevertheless, this topic has been fairly unexplored in the literature. In particular, we do not know how training affects turnover intention and how this influence is moderated by employee characteristics like membership (i.e., holding employer shares) and age. Thus, the aim of this article is to examine the impact of training on turnover intention, taking into account employee membership and age. Design/methodology/approach The research hypotheses were formulated using the framework of social exchange (SET) theory and were verified using a sample of more than 1,500 employees sourced from 42 Polish co-operative banks in 2017. The analysis involved two-level linear regression models with two- and three-way moderation. Findings The results indicate that training decreases turnover intention in CFIs. Moreover, this effect appears to be stronger for employee-members than for non-members. Furthermore, moderation through membership only applies to older employees, whereas, among younger employees, there is no difference between members and non-members. Originality/value By investigating the effects of training within CFIs specifically, this article responds to calls to take context into greater account in HRM studies, and also helps find moderators to explain the ambiguity of existing studies about the impact of training on turnover. Moreover, the article makes an important contribution to the co-operative literature by analysing the role of membership in shaping employee turnover intention.