A new approach to represent assembly called state matrix representation and an algorithm for automatic robot assembly planning based on this representation is proposed. The state matrix representation of assembly is configured by considering the inter-relationships of parts and objects involved in the initial and the goal structures. Thanks to this new representation, the planning lgorithm is straightforward and can be easily and efficiently implemented with simple matrix manipulation. Unlike other planning methods, the actions involved in the assembly process are not defined in advance but are generated at planning time. The syntax of actions are designed so that while directly reflecting the semantics of actions, they can be easily manipulated by the planner. Two examples of how to plan an assembly based on this representation are given in the paper.