Aimed at the problem that the traditional ART-2 neural network can not recognize a gradually chan-ging course, an eternal term memory(ETM)vector is introduced into ART-2 to simulate the function of human brain, i.e. the deep remembrance for the initial impression.. The eternal term memory vector is determined only by the initial vector that establishes category neuron node and is used to keep the remembrance for this vec-tor for ever. Two times of vigilance algorithm are put forward, and the posterior input vector must first pass the first vigilance of this eternal term memory vector, only succeeded has it the qualification to begin the second vigilance of long term memory vector. The long term memory vector can be revised only when both of the vigi-lances are passed. Results of recognition examples show that the improved ART-2 overcomes the defect of tradi-tional ART-2 and can recognize a gradually changing course effectively.