A kind of second2order algorithm---recursive approximate Newton algorithm was given by Karayian2 nis. The algorithm was simplified when it was formulated. Especially, the simplification to matrix Hessian was very reluctant, which led to the loss of valuable information and affected performance of the algorithm to certain extent. For multi2layer feed2forward neural networks, the second2order back2propagation recursive algorithm based generalized costcriteria was proposed. It is proved that it is equivalent to Newton recursive algorithm and has a second2order convergent rate. The performance and application prospect are analyzed. Lots of simulation ex2periments indicate that the calculation of the new algorithm is almost equivalent to the recursive least square multi2ple algorithm. The algorithm and selection of networks parameters are significant and the performance is more ex2cellent than BP algorithm and the second2order learning algorithm that was given by Karayiannis.