Scandals on online social networking have greatly raised privacy concerns regarding the massive amount of personal information stored on social networking platforms. The privacy issues are rooted in the current design of online social networking. On one hand, users have to share their personal information with social networking service providers for networking purposes. On the other hand, the sharing essentially allows the service providers to own the data, and the sharing may result in various privacy issues due to the business model of the service providers. In this paper, we propose RemoraBook to solve the privacy issues in online social networking with Remora Computing, inspired by remora fishes known for traveling effortlessly by attaching themselves to large marine animals such as sharks. Remora Computing enables RemoraBook users to utilize facilities available from service providers to build social networks without sharing information to service providers. The networking function and messaging function of RemoraBook are implemented based on Facebook and Gmail facilities respectively. Our extensive experiments on RemoraBook show that social networks can be reliably built in RemoraBook without significant degradation on usability.