We propose a novel associative memory that performs well on incremental learning and is robust to noisy data. Using the proposed method, new associative pairs presented sequentially can be learned accurately without forgetting previously learned patterns. The memory size of the proposed method increases adaptively. Therefore, it suffers neither redundancy nor insufficiency of memory size, even in an environment where the maximum number of associative pairs to be presented is unknown before learning. The proposed method deals with two types of noise. No conventional bidirectional associative memory deals with both types.