A new training algorithm for the chaotic Adachi Neural Network (AdNN) is investigated. The classical training algorithm for the AdNN and it's variants is usually a “one-shot” learning, for example, the Outer Product Rule (OPR) is the most used. Although the OPR is effective for conventional neural networks, its effectiveness and adequateness for Chaotic Neural Networks (CNNs) have not been discussed formally. As a complementary and tentative work in this field, we modified the AdNN's weights by enforcing an unsupervised Hebbian rule. Experimental analysis shows that the new weighted AdNN yields even stronger dynamical associative memory and pattern recognition phenomena for different settings than the primitive AdNN.