The potential of blockchain technology has received attention in the area of FinTech. Although a precise definition of blockchain technology has not yet been given, it is important to consider how to classify different blockchain systems in order to better understand their potential and limitations. The goal of this paper is to add to the discussion on blockchain technology by proposing a classification based on two dimensions external to the system: (1) existence of an authority and (2) incentive to participate in the blockchain. We define these dimensions and describe the characteristics of the blockchain systems belonging to each classification.