Every innovation begins as a deviation from existing social norms. Given the strong effect of social norms and pressure, how can any innovation ever diffuse to the point where it becomes a new social norm? The seeming paradox of how a minority can influence the majority has not been explained well by prevailing social science theory. Computer simulations of the diffusion of a new behavior within the social network of a Bangladesh village led to the discovery of a new principle of social change that resolves this paradox. The results revealed the important but overlooked role played by boundaries that emerge within a social network and how such local boundaries affect the creation of a new social norm. A minority position can become the social norm by means of the process of bounded normative influence. As long as a minority maintains its majority status within its own, locally bounded portion of the network, then it can survive, recruit converts in the near surround, and establish its behavior as the norm for the network as a whole. The process is accelerated when the minority subgroup is centrally located in the network and communicates more frequently and persuasively than the majority.