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In this paper, we reconsider and analyze our previous paper a novel hash algorithm construction based on chaotic neural network, then present equal-length and unequal-length forgery attacks against its security in detail, and then propose a significantly improved approach by utilizing a method of complicated nonlinear computation to enhance the security of the original hash algorithm. Theoretical analysis and computer simulation indicate that the improved algorithm can completely resist the two kinds of forgery attacks and also shows other better performance than the original one, such as better message and key sensitivity, statistical properties, which can satisfy the performance requirements of a more secure hash function. [ABSTRACT FROM AUTHOR]