Membranes are often composed of a mixture of amphiphilic molecules which aggregate into clusters or domains. A simple theoretical model is introduced which predicts that flat or weakly curved domains become unstable at a certain limiting size and then undergo a budding or invagination process. This shape transformation is primarily driven by the line tension of the domain edge. It is also predicted that the budding domain can rupture the membrane and then pinch off from the matrix. The size of the bud and the time scales involved in the budding dynamics are estimated for model membranes composed of lipid mixtures. This instability mechanism should also be effective for the budding of biomembranes