In this paper a new method of knowledge representation (area representation), and a new neural network based on it are proposed. Knowledge representation is the fundamental and important problem in the construction of an intelligent system. Local representation and distributed representation are typical examples but each has some merits and demerits. Area representation is intermediate between local and distributed representation and has the merits of both. The proposed novel neural network based on area representation uses the involution relation, where a lower-level concept is included in a higher-level concept and hierarchical-type representation of knowledge is possible. The network is formed by a number of Kohonen feature map layers that are coupled by a new learning algorithm known as neighborhood Hebbian learning, and as a whole, a multidirectional associative memory is constructed. The effectiveness of area representation and its implementation by neural networks are confirmed by computer simulation, where inheritance of knowledge from higher-level concept or recall from incomplete knowledge are investigated.