Concerns over the ever-increasing production, availability and use of multilayered individual data in social research, business and the everyday life calls for the development of ethical and legal guidelines. In parallel to civic and governmental initiatives, Critical Data Studies offers a transdisciplinary academic platform to define a common ethical framework for computational research. Essays recently published under this label argue for lines of conduct guided by principles such as fairness and justice. Cultural and evolutionary anthropology, as well as political psychology show, however, those principles are mostly common to Northern liberal cultures. For example, Moral Foundation Theory identifies five cross-cultural grounds to ethical reasoning—Fairness, Care, Authority, In-group and Purity—the first two being associated with progressive views, and the three others with traditionalist views. In the current development of Critical Data Studies, the framing of research ethics by fairness and justice therefore risks to maintain, if not increase, the hegemony of Northern researchers on scientific productivity in Big Data research. In this poster, I present a novel framing of Big Data ethics, one that considers the cross-cultural diversity of human morality. My objective is to lay out a shared ground to an urging global approach to knowledge production. First, I review existing ethical framework of Big Data research and classify each proposal according to the Moral Foundation Theory. Second, I identify commonalities and gaps of proposed framework and articulate possible extension of each framework using the missing moral foundations as guiding principles. Finally, I propose a synthetic framework of Big Data ethics. The poster highlights the unbalance of ethical considerations in Big Data research, and in scientific production in general. The proposed framework points at ethical stances that could become major concerns in future research using Big Data for social research: Political or economic definition of scientific objectives, applications and limitations (authority); Exclusion of individuals, groups and communities in the production, publication and application of research findings (in-group); Constrains on inter- and transdisciplinary collaborations, research topics, methods of analysis, epistemic positioning and ontological grounds (purity).